Lecture 5: Eigenvalues of Hermitians Matrices
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چکیده
This lecture takes a closer look at Hermitian matrices and at their eigenvalues. After a few generalities about Hermitian matrices, we prove a minimax and maximin characterization of their eigenvalues, known as Courant–Fischer theorem. We then derive some consequences of this characterization, such as Weyl theorem for the sum of two Hermitian matrices, an interlacing theorem for the sum of two Hermitian matrices, and an interlacing theorem for principal submatrices of Hermitian matrices.
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