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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

2 votes
2 answers
185 views

A problem of matrix polynomial expansion

The problem is $b = (1, -1)^\top, c = (1, 1)^\top, A \in \mathbb{R}^{2 \times 2}$, suppose the sum of reverse diagonal elements of $A$ is zero (i.e., $A_{12} + A_{21} = 0$), prove that the sum of re …
fs l's user avatar
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1 vote
Accepted

A problem of matrix polynomial expansion

Someone told me a simple method, I decide to post it here. Note that for any $A \in \mathbb{R}^{2 \times 2}$, $A_{12} + A_{21} = 0$ if and only if \begin{equation*} A^\top = \sigma^{-1} A \sigma \ …
fs l's user avatar
  • 81