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Arindama Singh ()
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Arindama Singh: Indian Institute of Technology Madras, Department of Mathematics

Chapter Chapter 6 in Introduction to Matrix Theory, 2021, pp 115-156 from Springer

Abstract: Abstract Eigenvalues and eigenvectors can be used to bring a matrix to nice forms using similarity transformations. One such useful form is Schur triangularization. This triangular form of a matrix is used to prove Cayley–Hamilton theorem. Further, it helps in characterizing matrices which are similar to a diagonal matrix. All matrices cannot be diagonalized, but each matrix is shown to be similar to a nearly diagonal matrix, called a Jordan matrix. Using the diagonalizability of Hermitian matrices a more general form of a matrix, called the Singular Value Decomposition is derived. From there, another useful form such as the Polar Decomposition of a matrix is obtained.

Date: 2021
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DOI: 10.1007/978-3-030-80481-7_6

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