Recent questions tagged trace-of-matrix

2 2 votes
1 1 answer
349
349 views
Let $B=\left(\left(b_{i, j}\right)\right)$ be an $n \times n$ matrix. Let $p:\{1,2, \ldots, n\} \mapsto\{1,2, \ldots, n\}$ be a bijection (i.e. a one-to-one corresponde...
3 3 votes
2 2 answers
405
405 views
Consider the collection $\mathcal{C}$ of all possible $n \times n$ matrices with entries in $\{1, \ldots, n\}$ that obey the following property: every row of $M$ is a per...
0 0 votes
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206 views
Let $n \geqslant 1$. Consider non-zero $n \times n$ real matrices $A$ such that $\operatorname{trace}(A X)=0$, for every real matrix $X$ with $\operatorname{trace}(X)=0$....
0 0 votes
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181
181 views
Let $T$ be an endomorphism of a finite dimensional real vector space $V$, and let $W$ denote the image of $T$. Let $T^{\prime}$ denote the restriction of $T$ to $W$. Then...
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