Comments on: Eigenvalues of a Hermitian Matrix are Real Numbers https://yutsumura.com/eigenvalues-of-a-hermitian-matrix-are-real-numbers/ Fri, 05 Jan 2018 17:56:18 +0000 hourly 1 https://wordpress.org/?v=5.3.4 By: A Hermitian Matrix Has Real Eigenvalues – David Tersegno's Laser Writeshow https://yutsumura.com/eigenvalues-of-a-hermitian-matrix-are-real-numbers/#comment-4949 Fri, 05 Jan 2018 17:56:18 +0000 https://yutsumura.com/?p=1475#comment-4949 […] seen proofs that Hermitian matrices have real eigenvalues. Here are a couple. These start by assuming there is some eigenvalue/eigenvector pair, and using the fact that a […]

]]> By: Inequality about Eigenvalue of a Real Symmetric Matrix – Problems in Mathematics https://yutsumura.com/eigenvalues-of-a-hermitian-matrix-are-real-numbers/#comment-1972 Sat, 29 Jul 2017 03:14:35 +0000 https://yutsumura.com/?p=1475#comment-1972 […] that all the eigenvalues of a symmetric matrices are real numbers. Let $lambda_1, dots, lambda_n$ be eigenvalues of […]

]]> By: Top 10 Popular Math Problems in 2016-2017 – Problems in Mathematics https://yutsumura.com/eigenvalues-of-a-hermitian-matrix-are-real-numbers/#comment-1865 Thu, 20 Jul 2017 01:56:22 +0000 https://yutsumura.com/?p=1475#comment-1865 […] The proof is given in the post Eigenvalues of a Hermitian Matrix are Real Numbers […]

]]> By: A Matrix Equation of a Symmetric Matrix and the Limit of its Solution – Problems in Mathematics https://yutsumura.com/eigenvalues-of-a-hermitian-matrix-are-real-numbers/#comment-1572 Thu, 15 Jun 2017 15:57:54 +0000 https://yutsumura.com/?p=1475#comment-1572 […] that the eigenvalues of a real symmetric matrices are all real numbers and it is diagonalizable by an orthogonal […]

]]> By: Positive definite real symmetric matrix and its eigenvalues – Problems in Mathematics https://yutsumura.com/eigenvalues-of-a-hermitian-matrix-are-real-numbers/#comment-1247 Sun, 30 Apr 2017 21:53:17 +0000 https://yutsumura.com/?p=1475#comment-1247 […] that the eigenvalues of a real symmetric matrix are real. (See the corollary in the post “Eigenvalues of a Hermitian matrix are real numbers“.) Let $lambda$ be a (real) eigenvalue of $A$ and let $mathbf{x}$ be a corresponding real […]

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