query: Prove or disprove: If $A$ and $B$ are non-negative definite matrices then $AB$ is diagonalizable
positive_passages.docid: 29454
positive_passages.text: A and B are real, symmetric and positive semi-definite matrices of the same order; is AB diagonalizable?
negative_passages.docid: 72541
negative_passages.text: Is the matrix diagonalizable for all values of t?
negative_passages.docid: 40222
negative_passages.text: Matrices that are not diagonal or triangular, whose eigenvalues are the diagonal elements
negative_passages.docid: 73697
negative_passages.text: Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
negative_passages.docid: 38945
negative_passages.text: On the proof that the product of diagonal matrices is a diagonal matrix?
negative_passages.docid: 98631
negative_passages.text: Postive-semidefiniteness of matrix with entries $1/(a_i+a_j)$
negative_passages.docid: 119387
negative_passages.text: If $A$ is any matrix then $A^*A$ and $AA^*$ are Hermitian with non-negative eigenvalues
negative_passages.docid: 87262
negative_passages.text: How to prove positive semidefiniteness of two matrices through Schur Complement?
negative_passages.docid: 114208
negative_passages.text: Does non-symmetric positive definite matrix have positive eigenvalues?
negative_passages.docid: 36567
negative_passages.text: $A^{T}A$ positive definite then A is invertible?
negative_passages.docid: 59402
negative_passages.text: Comparing Eigenvalues of Positive Semidefinite Matrices
negative_passages.docid: 35834
negative_passages.text: Is the product of any two invertible diagonalizable matrices diagonalizable?
negative_passages.docid: 71833
negative_passages.text: Are idempotent matrices always diagonalizable?
negative_passages.docid: 33448
negative_passages.text: Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
negative_passages.docid: 15969
negative_passages.text: How to prove that $A$ is positive semi-definite if all principal minors are non-negative?
negative_passages.docid: 46308
negative_passages.text: Simultaneous diagonlisation of two quadratic forms, one of which is positive definite
negative_passages.docid: 10828
negative_passages.text: If $A^2 = I$, then $A$ is diagonalizable, and is $I$ if $1$ is its only eigenvalue