Short Proofs of Theorems of Horn and Mirsky on Diagonals and Eigenvalues of Matrices
نویسنده
چکیده
Horn’s Theorem plays an important role in the theory of matrix majorization and elsewhere. We give a simple proof of it, as well as a related theorem of Mirsky.
منابع مشابه
Ela Short Proofs of Theorems of Mirsky and Horn on Diagonals and Eigenvalues of Matrices∗
A theorem of Mirsky provides necessary and sufficient conditions for the existence of an N-square complex matrix with prescribed diagonal entries and prescribed eigenvalues. A simple inductive proof of this theorem is given.
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A theorem of Mirsky provides necessary and sufficient conditions for the existence of an N-square complex matrix with prescribed diagonal entries and prescribed eigenvalues. A simple inductive proof of this theorem is given.
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