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Results tagged with linear-algebra
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user 103308
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
1
vote
1
answer
103
views
tighter bound on the sum of sub-matrices
Suppose $A = [A_1, A_2, \ldots, A_n]$ is a matrix, and each $A_i$ is a column-wise sub-matrix of $A$. Given a vector $v \in \mathbb{R}^n$, a bound of $\| \sum_{i=1}^n A_i v_i \|_2$ (spectral norm) in …
- 85
7
votes
1
answer
673
views
Orthogonality of positive (semi-)definite matrices
Given positive semidefinite matrices $A,B \succeq 0$, $A, B \in \mathbb{R}^{n \times n}$, if we have $$\langle A, B \rangle = 0,$$ where $\langle \cdot, \cdot \rangle$ denotes the Frobenius inner prod …
- 85