Singular value decomposition (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Singular value decomposition" in English language version.

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25doi.org

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alterlab.org

Bertagnolli, N. M.; Drake, J. A.; Tennessen, J. M.; Alter, O. (November 2013). "SVD Identifies Transcript Length Distribution Functions from DNA Microarray Data and Reveals Evolutionary Forces Globally Affecting GBM Metabolism". PLOS ONE. 8 (11): e78913. Bibcode:2013PLoSO...878913B. doi:10.1371/journal.pone.0078913. PMC 3839928. PMID 24282503. Highlight.

ams.org

mathscinet.ams.org

Hestenes, M. R. (1958). "Inversion of Matrices by Biorthogonalization and Related Results". Journal of the Society for Industrial and Applied Mathematics. 6 (1): 51–90. doi:10.1137/0106005. JSTOR 2098862. MR 0092215.
Golub, G. H.; Reinsch, C. (1970). "Singular value decomposition and least squares solutions". Numerische Mathematik. 14 (5): 403–420. doi:10.1007/BF02163027. MR 1553974. S2CID 123532178.

arxiv.org

Setyawati, Y.; Ohme, F.; Khan, S. (2019). "Enhancing gravitational waveform model through dynamic calibration". Physical Review D. 99 (2): 024010. arXiv:1810.07060. Bibcode:2019PhRvD..99b4010S. doi:10.1103/PhysRevD.99.024010. S2CID 118935941.
Bosagh Zadeh, Reza; Carlsson, Gunnar (2013). "Dimension Independent Matrix Square Using MapReduce". arXiv:1304.1467 [cs.DS].
Hadi Fanaee Tork; João Gama (September 2014). "Eigenspace method for spatiotemporal hotspot detection". Expert Systems. 32 (3): 454–464. arXiv:1406.3506. Bibcode:2014arXiv1406.3506F. doi:10.1111/exsy.12088. S2CID 15476557.
Hadi Fanaee Tork; João Gama (May 2015). "EigenEvent: An Algorithm for Event Detection from Complex Data Streams in Syndromic Surveillance". Intelligent Data Analysis. 19 (3): 597–616. arXiv:1406.3496. doi:10.3233/IDA-150734. S2CID 17966555.
Albers, Jasper; Kurth, Anno; Gutzen, Robin; Morales-Gregorio, Aitor; Denker, Michael; Gruen, Sonja; van Albada, Sacha; Diesmann, Markus (2025). "Assessing the Similarity of Real Matrices with Arbitrary Shape". PRX Life (3): 023005. arXiv:2403.17687. doi:10.1103/PRXLife.3.023005.

doi.org

DeAngelis, G. C.; Ohzawa, I.; Freeman, R. D. (October 1995). "Receptive-field dynamics in the central visual pathways". Trends Neurosci. 18 (10): 451–8. doi:10.1016/0166-2236(95)94496-R. PMID 8545912. S2CID 12827601.
Depireux, D. A.; Simon, J. Z.; Klein, D. J.; Shamma, S. A. (March 2001). "Spectro-temporal response field characterization with dynamic ripples in ferret primary auditory cortex". J. Neurophysiol. 85 (3): 1220–34. doi:10.1152/jn.2001.85.3.1220. PMID 11247991.
Sahidullah, Md.; Kinnunen, Tomi (March 2016). "Local spectral variability features for speaker verification". Digital Signal Processing. 50: 1–11. Bibcode:2016DSP....50....1S. doi:10.1016/j.dsp.2015.10.011.
Mademlis, Ioannis; Tefas, Anastasios; Pitas, Ioannis (2018). "Regularized SVD-Based Video Frame Saliency for Unsupervised Activity Video Summarization". 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE. pp. 2691–2695. doi:10.1109/ICASSP.2018.8462274. ISBN 978-1-5386-4658-8. S2CID 52286352. Retrieved 19 January 2023.
O. Alter, P. O. Brown and D. Botstein (September 2000). "Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling". PNAS. 97 (18): 10101–10106. Bibcode:2000PNAS...9710101A. doi:10.1073/pnas.97.18.10101. PMC 27718. PMID 10963673.
O. Alter; G. H. Golub (November 2004). "Integrative Analysis of Genome-Scale Data by Using Pseudoinverse Projection Predicts Novel Correlation Between DNA Replication and RNA Transcription". PNAS. 101 (47): 16577–16582. Bibcode:2004PNAS..10116577A. doi:10.1073/pnas.0406767101. PMC 534520. PMID 15545604.
O. Alter; G. H. Golub (August 2006). "Singular Value Decomposition of Genome-Scale mRNA Lengths Distribution Reveals Asymmetry in RNA Gel Electrophoresis Band Broadening". PNAS. 103 (32): 11828–11833. Bibcode:2006PNAS..10311828A. doi:10.1073/pnas.0604756103. PMC 1524674. PMID 16877539.
Bertagnolli, N. M.; Drake, J. A.; Tennessen, J. M.; Alter, O. (November 2013). "SVD Identifies Transcript Length Distribution Functions from DNA Microarray Data and Reveals Evolutionary Forces Globally Affecting GBM Metabolism". PLOS ONE. 8 (11): e78913. Bibcode:2013PLoSO...878913B. doi:10.1371/journal.pone.0078913. PMC 3839928. PMID 24282503. Highlight.
Edelman, Alan (1992). "On the distribution of a scaled condition number" (PDF). Math. Comp. 58 (197): 185–190. Bibcode:1992MaCom..58..185E. doi:10.1090/S0025-5718-1992-1106966-2.
Shen, Jianhong (Jackie) (2001). "On the singular values of Gaussian random matrices". Linear Alg. Appl. 326 (1–3): 1–14. doi:10.1016/S0024-3795(00)00322-0.
Walton, S.; Hassan, O.; Morgan, K. (2013). "Reduced order modelling for unsteady fluid flow using proper orthogonal decomposition and radial basis functions". Applied Mathematical Modelling. 37 (20–21): 8930–8945. doi:10.1016/j.apm.2013.04.025.
Setyawati, Y.; Ohme, F.; Khan, S. (2019). "Enhancing gravitational waveform model through dynamic calibration". Physical Review D. 99 (2): 024010. arXiv:1810.07060. Bibcode:2019PhRvD..99b4010S. doi:10.1103/PhysRevD.99.024010. S2CID 118935941.
Hadi Fanaee Tork; João Gama (September 2014). "Eigenspace method for spatiotemporal hotspot detection". Expert Systems. 32 (3): 454–464. arXiv:1406.3506. Bibcode:2014arXiv1406.3506F. doi:10.1111/exsy.12088. S2CID 15476557.
Hadi Fanaee Tork; João Gama (May 2015). "EigenEvent: An Algorithm for Event Detection from Complex Data Streams in Syndromic Surveillance". Intelligent Data Analysis. 19 (3): 597–616. arXiv:1406.3496. doi:10.3233/IDA-150734. S2CID 17966555.
Muralidharan, Vivek; Howell, Kathleen (2023). "Stretching directions in cislunar space: Applications for departures and transfer design". Astrodynamics. 7 (2): 153–178. Bibcode:2023AsDyn...7..153M. doi:10.1007/s42064-022-0147-z. S2CID 252637213.
Muralidharan, Vivek; Howell, Kathleen (2022). "Leveraging stretching directions for stationkeeping in Earth-Moon halo orbits". Advances in Space Research. 69 (1): 620–646. Bibcode:2022AdSpR..69..620M. doi:10.1016/j.asr.2021.10.028. S2CID 239490016.
Albers, Jasper; Kurth, Anno; Gutzen, Robin; Morales-Gregorio, Aitor; Denker, Michael; Gruen, Sonja; van Albada, Sacha; Diesmann, Markus (2025). "Assessing the Similarity of Real Matrices with Arbitrary Shape". PRX Life (3): 023005. arXiv:2403.17687. doi:10.1103/PRXLife.3.023005.
Rijk, P.P.M. de (1989). "A one-sided Jacobi algorithm for computing the singular value decomposition on a vector computer". SIAM J. Sci. Stat. Comput. 10 (2): 359–371. doi:10.1137/0910023.
Demmel, James (2000). "Decompositions". Templates for the Solution of Algebraic Eigenvalue Problems. By Bai, Zhaojun; Demmel, James; Dongarra, Jack J.; Ruhe, Axel; van der Vorst, Henk A. Society for Industrial and Applied Mathematics. doi:10.1137/1.9780898719581. ISBN 978-0-89871-471-5.
Chicco, D; Masseroli, M (2015). "Software suite for gene and protein annotation prediction and similarity search". IEEE/ACM Transactions on Computational Biology and Bioinformatics. 12 (4): 837–843. doi:10.1109/TCBB.2014.2382127. hdl:11311/959408. PMID 26357324. S2CID 14714823.
Fan, Ky. (1951). "Maximum properties and inequalities for the eigenvalues of completely continuous operators". Proceedings of the National Academy of Sciences of the United States of America. 37 (11): 760–766. Bibcode:1951PNAS...37..760F. doi:10.1073/pnas.37.11.760. PMC 1063464. PMID 16578416.
Eckart, C.; Young, G. (1936). "The approximation of one matrix by another of lower rank". Psychometrika. 1 (3): 211–8. doi:10.1007/BF02288367. S2CID 10163399.
Hestenes, M. R. (1958). "Inversion of Matrices by Biorthogonalization and Related Results". Journal of the Society for Industrial and Applied Mathematics. 6 (1): 51–90. doi:10.1137/0106005. JSTOR 2098862. MR 0092215.
(Golub & Kahan 1965) Golub, Gene H.; Kahan, William (1965). "Calculating the singular values and pseudo-inverse of a matrix". Journal of the Society for Industrial and Applied Mathematics, Series B: Numerical Analysis. 2 (2): 205–224. Bibcode:1965SJNA....2..205G. doi:10.1137/0702016. JSTOR 2949777.
Golub, G. H.; Reinsch, C. (1970). "Singular value decomposition and least squares solutions". Numerische Mathematik. 14 (5): 403–420. doi:10.1007/BF02163027. MR 1553974. S2CID 123532178.

dtic.mil

apps.dtic.mil

Sarwar, Badrul; Karypis, George; Konstan, Joseph A. & Riedl, John T. (2000). Application of Dimensionality Reduction in Recommender System – A Case Study (Technical report 00-043). University of Minnesota. hdl:11299/215429.

handle.net

hdl.handle.net

Sarwar, Badrul; Karypis, George; Konstan, Joseph A. & Riedl, John T. (2000). Application of Dimensionality Reduction in Recommender System – A Case Study (Technical report 00-043). University of Minnesota. hdl:11299/215429.
Chicco, D; Masseroli, M (2015). "Software suite for gene and protein annotation prediction and similarity search". IEEE/ACM Transactions on Computational Biology and Bioinformatics. 12 (4): 837–843. doi:10.1109/TCBB.2014.2382127. hdl:11311/959408. PMID 26357324. S2CID 14714823.

harvard.edu

ui.adsabs.harvard.edu

Sahidullah, Md.; Kinnunen, Tomi (March 2016). "Local spectral variability features for speaker verification". Digital Signal Processing. 50: 1–11. Bibcode:2016DSP....50....1S. doi:10.1016/j.dsp.2015.10.011.
O. Alter, P. O. Brown and D. Botstein (September 2000). "Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling". PNAS. 97 (18): 10101–10106. Bibcode:2000PNAS...9710101A. doi:10.1073/pnas.97.18.10101. PMC 27718. PMID 10963673.
O. Alter; G. H. Golub (November 2004). "Integrative Analysis of Genome-Scale Data by Using Pseudoinverse Projection Predicts Novel Correlation Between DNA Replication and RNA Transcription". PNAS. 101 (47): 16577–16582. Bibcode:2004PNAS..10116577A. doi:10.1073/pnas.0406767101. PMC 534520. PMID 15545604.
O. Alter; G. H. Golub (August 2006). "Singular Value Decomposition of Genome-Scale mRNA Lengths Distribution Reveals Asymmetry in RNA Gel Electrophoresis Band Broadening". PNAS. 103 (32): 11828–11833. Bibcode:2006PNAS..10311828A. doi:10.1073/pnas.0604756103. PMC 1524674. PMID 16877539.
Bertagnolli, N. M.; Drake, J. A.; Tennessen, J. M.; Alter, O. (November 2013). "SVD Identifies Transcript Length Distribution Functions from DNA Microarray Data and Reveals Evolutionary Forces Globally Affecting GBM Metabolism". PLOS ONE. 8 (11): e78913. Bibcode:2013PLoSO...878913B. doi:10.1371/journal.pone.0078913. PMC 3839928. PMID 24282503. Highlight.
Edelman, Alan (1992). "On the distribution of a scaled condition number" (PDF). Math. Comp. 58 (197): 185–190. Bibcode:1992MaCom..58..185E. doi:10.1090/S0025-5718-1992-1106966-2.
Setyawati, Y.; Ohme, F.; Khan, S. (2019). "Enhancing gravitational waveform model through dynamic calibration". Physical Review D. 99 (2): 024010. arXiv:1810.07060. Bibcode:2019PhRvD..99b4010S. doi:10.1103/PhysRevD.99.024010. S2CID 118935941.
Hadi Fanaee Tork; João Gama (September 2014). "Eigenspace method for spatiotemporal hotspot detection". Expert Systems. 32 (3): 454–464. arXiv:1406.3506. Bibcode:2014arXiv1406.3506F. doi:10.1111/exsy.12088. S2CID 15476557.
Muralidharan, Vivek; Howell, Kathleen (2023). "Stretching directions in cislunar space: Applications for departures and transfer design". Astrodynamics. 7 (2): 153–178. Bibcode:2023AsDyn...7..153M. doi:10.1007/s42064-022-0147-z. S2CID 252637213.
Muralidharan, Vivek; Howell, Kathleen (2022). "Leveraging stretching directions for stationkeeping in Earth-Moon halo orbits". Advances in Space Research. 69 (1): 620–646. Bibcode:2022AdSpR..69..620M. doi:10.1016/j.asr.2021.10.028. S2CID 239490016.
Fan, Ky. (1951). "Maximum properties and inequalities for the eigenvalues of completely continuous operators". Proceedings of the National Academy of Sciences of the United States of America. 37 (11): 760–766. Bibcode:1951PNAS...37..760F. doi:10.1073/pnas.37.11.760. PMC 1063464. PMID 16578416.
(Golub & Kahan 1965) Golub, Gene H.; Kahan, William (1965). "Calculating the singular values and pseudo-inverse of a matrix". Journal of the Society for Industrial and Applied Mathematics, Series B: Numerical Analysis. 2 (2): 205–224. Bibcode:1965SJNA....2..205G. doi:10.1137/0702016. JSTOR 2949777.

ieee.org

ieeexplore.ieee.org

Mademlis, Ioannis; Tefas, Anastasios; Pitas, Ioannis (2018). "Regularized SVD-Based Video Frame Saliency for Unsupervised Activity Video Summarization". 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE. pp. 2691–2695. doi:10.1109/ICASSP.2018.8462274. ISBN 978-1-5386-4658-8. S2CID 52286352. Retrieved 19 January 2023.

jstor.org

Hestenes, M. R. (1958). "Inversion of Matrices by Biorthogonalization and Related Results". Journal of the Society for Industrial and Applied Mathematics. 6 (1): 51–90. doi:10.1137/0106005. JSTOR 2098862. MR 0092215.
(Golub & Kahan 1965) Golub, Gene H.; Kahan, William (1965). "Calculating the singular values and pseudo-inverse of a matrix". Journal of the Society for Industrial and Applied Mathematics, Series B: Numerical Analysis. 2 (2): 205–224. Bibcode:1965SJNA....2..205G. doi:10.1137/0702016. JSTOR 2949777.

mathworks.co.kr

mathworks.co.kr/matlabcentral/fileexchange/12674-simple-svd

missouri.edu

faculty.missouri.edu

Uhlmann, Jeffrey (2018). A Generalized Matrix Inverse that is Consistent with Respect to Diagonal Transformations (PDF). SIAM Journal on Matrix Analysis. Vol. 239. pp. 781–800. Archived from the original (PDF) on 17 June 2019.

mit.edu

math.mit.edu

Edelman, Alan (1992). "On the distribution of a scaled condition number" (PDF). Math. Comp. 58 (197): 185–190. Bibcode:1992MaCom..58..185E. doi:10.1090/S0025-5718-1992-1106966-2.

netlib.org

Netlib.org
Netlib.org
Demmel, James (2000). "Decompositions". Templates for the Solution of Algebraic Eigenvalue Problems. By Bai, Zhaojun; Demmel, James; Dongarra, Jack J.; Ruhe, Axel; van der Vorst, Henk A. Society for Industrial and Applied Mathematics. doi:10.1137/1.9780898719581. ISBN 978-0-89871-471-5.

nih.gov

pubmed.ncbi.nlm.nih.gov

DeAngelis, G. C.; Ohzawa, I.; Freeman, R. D. (October 1995). "Receptive-field dynamics in the central visual pathways". Trends Neurosci. 18 (10): 451–8. doi:10.1016/0166-2236(95)94496-R. PMID 8545912. S2CID 12827601.
Depireux, D. A.; Simon, J. Z.; Klein, D. J.; Shamma, S. A. (March 2001). "Spectro-temporal response field characterization with dynamic ripples in ferret primary auditory cortex". J. Neurophysiol. 85 (3): 1220–34. doi:10.1152/jn.2001.85.3.1220. PMID 11247991.
O. Alter, P. O. Brown and D. Botstein (September 2000). "Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling". PNAS. 97 (18): 10101–10106. Bibcode:2000PNAS...9710101A. doi:10.1073/pnas.97.18.10101. PMC 27718. PMID 10963673.
O. Alter; G. H. Golub (November 2004). "Integrative Analysis of Genome-Scale Data by Using Pseudoinverse Projection Predicts Novel Correlation Between DNA Replication and RNA Transcription". PNAS. 101 (47): 16577–16582. Bibcode:2004PNAS..10116577A. doi:10.1073/pnas.0406767101. PMC 534520. PMID 15545604.
O. Alter; G. H. Golub (August 2006). "Singular Value Decomposition of Genome-Scale mRNA Lengths Distribution Reveals Asymmetry in RNA Gel Electrophoresis Band Broadening". PNAS. 103 (32): 11828–11833. Bibcode:2006PNAS..10311828A. doi:10.1073/pnas.0604756103. PMC 1524674. PMID 16877539.
Bertagnolli, N. M.; Drake, J. A.; Tennessen, J. M.; Alter, O. (November 2013). "SVD Identifies Transcript Length Distribution Functions from DNA Microarray Data and Reveals Evolutionary Forces Globally Affecting GBM Metabolism". PLOS ONE. 8 (11): e78913. Bibcode:2013PLoSO...878913B. doi:10.1371/journal.pone.0078913. PMC 3839928. PMID 24282503. Highlight.
Chicco, D; Masseroli, M (2015). "Software suite for gene and protein annotation prediction and similarity search". IEEE/ACM Transactions on Computational Biology and Bioinformatics. 12 (4): 837–843. doi:10.1109/TCBB.2014.2382127. hdl:11311/959408. PMID 26357324. S2CID 14714823.
Fan, Ky. (1951). "Maximum properties and inequalities for the eigenvalues of completely continuous operators". Proceedings of the National Academy of Sciences of the United States of America. 37 (11): 760–766. Bibcode:1951PNAS...37..760F. doi:10.1073/pnas.37.11.760. PMC 1063464. PMID 16578416.

ncbi.nlm.nih.gov

O. Alter, P. O. Brown and D. Botstein (September 2000). "Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling". PNAS. 97 (18): 10101–10106. Bibcode:2000PNAS...9710101A. doi:10.1073/pnas.97.18.10101. PMC 27718. PMID 10963673.
O. Alter; G. H. Golub (November 2004). "Integrative Analysis of Genome-Scale Data by Using Pseudoinverse Projection Predicts Novel Correlation Between DNA Replication and RNA Transcription". PNAS. 101 (47): 16577–16582. Bibcode:2004PNAS..10116577A. doi:10.1073/pnas.0406767101. PMC 534520. PMID 15545604.
O. Alter; G. H. Golub (August 2006). "Singular Value Decomposition of Genome-Scale mRNA Lengths Distribution Reveals Asymmetry in RNA Gel Electrophoresis Band Broadening". PNAS. 103 (32): 11828–11833. Bibcode:2006PNAS..10311828A. doi:10.1073/pnas.0604756103. PMC 1524674. PMID 16877539.
Bertagnolli, N. M.; Drake, J. A.; Tennessen, J. M.; Alter, O. (November 2013). "SVD Identifies Transcript Length Distribution Functions from DNA Microarray Data and Reveals Evolutionary Forces Globally Affecting GBM Metabolism". PLOS ONE. 8 (11): e78913. Bibcode:2013PLoSO...878913B. doi:10.1371/journal.pone.0078913. PMC 3839928. PMID 24282503. Highlight.
Fan, Ky. (1951). "Maximum properties and inequalities for the eigenvalues of completely continuous operators". Proceedings of the National Academy of Sciences of the United States of America. 37 (11): 760–766. Bibcode:1951PNAS...37..760F. doi:10.1073/pnas.37.11.760. PMC 1063464. PMID 16578416.

semanticscholar.org

api.semanticscholar.org

DeAngelis, G. C.; Ohzawa, I.; Freeman, R. D. (October 1995). "Receptive-field dynamics in the central visual pathways". Trends Neurosci. 18 (10): 451–8. doi:10.1016/0166-2236(95)94496-R. PMID 8545912. S2CID 12827601.
Mademlis, Ioannis; Tefas, Anastasios; Pitas, Ioannis (2018). "Regularized SVD-Based Video Frame Saliency for Unsupervised Activity Video Summarization". 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE. pp. 2691–2695. doi:10.1109/ICASSP.2018.8462274. ISBN 978-1-5386-4658-8. S2CID 52286352. Retrieved 19 January 2023.
Setyawati, Y.; Ohme, F.; Khan, S. (2019). "Enhancing gravitational waveform model through dynamic calibration". Physical Review D. 99 (2): 024010. arXiv:1810.07060. Bibcode:2019PhRvD..99b4010S. doi:10.1103/PhysRevD.99.024010. S2CID 118935941.
Hadi Fanaee Tork; João Gama (September 2014). "Eigenspace method for spatiotemporal hotspot detection". Expert Systems. 32 (3): 454–464. arXiv:1406.3506. Bibcode:2014arXiv1406.3506F. doi:10.1111/exsy.12088. S2CID 15476557.
Hadi Fanaee Tork; João Gama (May 2015). "EigenEvent: An Algorithm for Event Detection from Complex Data Streams in Syndromic Surveillance". Intelligent Data Analysis. 19 (3): 597–616. arXiv:1406.3496. doi:10.3233/IDA-150734. S2CID 17966555.
Muralidharan, Vivek; Howell, Kathleen (2023). "Stretching directions in cislunar space: Applications for departures and transfer design". Astrodynamics. 7 (2): 153–178. Bibcode:2023AsDyn...7..153M. doi:10.1007/s42064-022-0147-z. S2CID 252637213.
Muralidharan, Vivek; Howell, Kathleen (2022). "Leveraging stretching directions for stationkeeping in Earth-Moon halo orbits". Advances in Space Research. 69 (1): 620–646. Bibcode:2022AdSpR..69..620M. doi:10.1016/j.asr.2021.10.028. S2CID 239490016.
Chicco, D; Masseroli, M (2015). "Software suite for gene and protein annotation prediction and similarity search". IEEE/ACM Transactions on Computational Biology and Bioinformatics. 12 (4): 837–843. doi:10.1109/TCBB.2014.2382127. hdl:11311/959408. PMID 26357324. S2CID 14714823.
Eckart, C.; Young, G. (1936). "The approximation of one matrix by another of lower rank". Psychometrika. 1 (3): 211–8. doi:10.1007/BF02288367. S2CID 10163399.
Golub, G. H.; Reinsch, C. (1970). "Singular value decomposition and least squares solutions". Numerische Mathematik. 14 (5): 403–420. doi:10.1007/BF02163027. MR 1553974. S2CID 123532178.

ucdavis.edu

cs.ucdavis.edu

Demmel, James (2000). "Decompositions". Templates for the Solution of Algebraic Eigenvalue Problems. By Bai, Zhaojun; Demmel, James; Dongarra, Jack J.; Ruhe, Axel; van der Vorst, Henk A. Society for Industrial and Applied Mathematics. doi:10.1137/1.9780898719581. ISBN 978-0-89871-471-5.

uef.fi

erepo.uef.fi

Sahidullah, Md.; Kinnunen, Tomi (March 2016). "Local spectral variability features for speaker verification". Digital Signal Processing. 50: 1–11. Bibcode:2016DSP....50....1S. doi:10.1016/j.dsp.2015.10.011.

web.archive.org

Uhlmann, Jeffrey (2018). A Generalized Matrix Inverse that is Consistent with Respect to Diagonal Transformations (PDF). SIAM Journal on Matrix Analysis. Vol. 239. pp. 781–800. Archived from the original (PDF) on 17 June 2019.

wou.edu

The Singular Value Decomposition in Symmetric (Lowdin) Orthogonalization and Data Compression