Question

How eigenvalues are related to symmetrics and asymmetric matrox?

Answer 1

Eigenvalues for symmetric and skew-symmetric part of a matrix. Every real matrix can be decomposed into symmetric and skew-symmetric part. Symmetric matrix has only real numbers as its eigenvalues (including ) and skew-symmetric matrix has only imaginary values (also including ).

Answer 2

A has exactly n (not necessarily distinct) eigenvalues. There exists a set of n eigenvectors, one for each eigenvalue, that are mututally orthogonal.

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