Spectral Theorem: Diagonalizable Symmetric Matrix

Noriebelle Balbontin

doi:10.5281/zenodo.7140908

Research Article

Spectral Theorem: Diagonalizable Symmetric Matrix

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Noriebelle Balbontin

Psych Educ Multidisc J, 2022, 4 (7), 727-728, doi: 10.5281/zenodo.7140908, ISSN 2822-4353

Abstract

In linear algebra, is the canonical forms of a linear transformation. Given a particularly nice basis for the vector spaces in which one is working, the matrix of a linear transformation may also be particularly nice, revealing some information about how the transformation operates on the vector space.The spectral theorem provides a sufficient criterion for the existence of a particular canonical form. Specifically, the spectral theorem states that if A equals the transpose of A, then A is diagonalizable: there exists an invertible matrix B such that B-1 AB is a diagonal matrix.

Keywords: linear algebra, canonical forms, Spectral Theorem, Symmetric Matrix, Diagonalizable

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Bibliographic Information

Noriebelle Balbontin (2022). Spectral Theorem: Diagonalizable Symmetric Matrix, Psychology and Education: A Multidisciplinary Journal, 4(7): 727-728

Bibtex Citation


                        
            @article{noriebelle_balbontin2022pemj,

                author       = {Noriebelle Balbontin},

                title        = {Spectral Theorem: Diagonalizable Symmetric Matrix},

                journal      = {Psychology and Education: A Multidisciplinary Journal},

                year         = {2022},

                volume       = {4},

                number       = {7},

                pages        = {727-728},

                doi          = {10.5281/zenodo.7140908},

                url          = {https://scimatic.org/show_manuscript/641}

              }

APA Citation

Balbontin, N., (2022). Spectral Theorem: Diagonalizable Symmetric Matrix. Psychology and Education: A Multidisciplinary Journal, 4(7), 727-728. https://doi.org/10.5281/zenodo.7140908

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Spectral Theorem: Diagonalizable Symmetric Matrix

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