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Results tagged with matrix-analysis
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user 88133
The study of the properties of real and complex matrices that are more close to analysis and operator theory. For instance: the properties of positive definite matrices, matrix inequalities, perturbation analysis, matrix functions, inequalities between eigenvectors and singular values, majorization.
2
votes
The functional equation $T(x\otimes y)=T(x)\otimes T(y)$ on the matrix algebra
What is a linear operator---do you require $T_n(X_1 X_2) = T_n(X_1) T_n(X_2)$? If not, $T_n(X) = c^n X$ for a fixed scalar $c$ works. Even if yes, I think that $T_n(X) = X$ if $n$ odd, $0$ if $n$ even …
- 6,237
1
vote
The rank of the Hadamard product
Say $E$ contains a nonzero transversal (I welcome any suggestions of better terminology) if there is a collection of entries of $E$ with the properties (1) no two of the entries are in the same row or …
- 6,237
1
vote
About local maxima of multivariable polynomials
The set of critical points (in the domain) of a polynomial is the solution set of a system of polynomial equations viz the vanishing of the first derivatives. So it has finitely many irreducible compo …
- 6,237