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Results tagged with matrix-theory
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Matrix theory is the study of matrices as concrete objects, rather than as abstract linear operators between vector spaces (whose study belongs to linear algebra). For instance, this involves matrix factorizations and decompositions, nonnegative matrices and Perron-Frobenius theory, Schur complements, structured and special matrices, matrix functions and equations.
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An $n \times n$ matrix $A$ is similar to its transpose $A^{\top}$: elementary proof?
A famous result in linear algebra is the following.
An $n \times n$ matrix $A$ over a field $\mathbb{F}$ is similar to its transpose $A^T$.
I know one proof using the Smith Normal Form (SNF). Ho …
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