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The eigen values of a real symmetric matrix are all real.

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Q: What is the eigen value of a real symmetric matrix?
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What is the definition of a Hermitian matrix?

Hermitian matrix defined:If a square matrix, A, is equal to its conjugate transpose, A†, then A is a Hermitian matrix.Notes:1. The main diagonal elements of a Hermitian matrix must be real.2. The cross elements of a Hermitian matrix are complex numbers having equal real part values, and equal-in-magnitude-but-opposite-in-sign imaginary parts.


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Skew-Hermitian matrix defined:If the conjugate transpose, A†, of a square matrix, A, is equal to its negative, -A, then A is a skew-Hermitian matrix.Notes:1. The main diagonal elements of a skew-Hermitian matrix must be purely imaginary, including zero.2. The cross elements of a skew-Hermitian matrix are complex numbers having equal imaginary part values, and equal-in-magnitude-but-opposite-in-sign real parts.


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The singular value decomposition is a component of a real complicated matrix with many useful applications in signal processing and statistics. The singular value decomposition and the eigen decomposition are very closely related.


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What is the definition of a Hermitian matrix?

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