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Is a diagonal matrix positive Semidefinite?

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M is congruent with a diagonal matrix with positive real entries. M is symmetric or Hermitian, and all its eigenvalues are real and positive . M is symmetric or Hermitian, and all its leading principal minors are positive.
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2017年4月14日1 个回答
Let A be a symmetric diagonal matrix in which (A)ii≥0. Should one conclude that this matrix is positive semidefinite?

Semidefinite & Definite: Let A be a symmetric matrix. We say that A is (positive) semidefinite, and write A ≽ 0, if all eigenvalues of A are nonnegative.
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It means that any symmetric matrix M = UT DU. Here D is the diagonal matrix with eigenvalues and U is the matrix with columns as eigenvectors. Exercise 7. Show ...
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2015年7月31日1 个回答
Consider the set Dn of n-dimensional positive semidefinite matrices. A matrix M∈Dn is called ϵ diagonal in trace distance if there is a diagonal ...
Definition: The symmetric matrix A is said positive semidefinite (A ≥ 0) if all its eigenvalues are non negative. Theorem: If A is positive definite ...
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The next lemma shows what happens to the spectrum of a positive semidefinite matrix if a skew symmetric matrix is added to it, in the case where the eigenvalues ...
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A symmetric matrix that is not definite is said to be indefinite. With respect to the diagonal elements of real symmetric and positive (semi)definite matrices ...
Every symmetric positive definite matrix A has a unique factorization of the form. A = LLt, where L is a lower triangular matrix with positive diagonal entries.
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2015年11月28日11 个回答
Say A=B*B^H (^H means conjugate transition) C=A - (diagonal of A). So C is a symmetric matrix which diagonal entries are all 0. I wondering whether there ...