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Recent questions tagged trace-of-matrix
2
2 votes
1
1 answer
349
349 views
CMI Data Science 2025 | Part A | Question: 7
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...
Shubham Sharma 2
349
views
asked
Jun 20, 2025
Linear Algebra
cmi2025-datascience
linear-algebra
matrix
trace-of-matrix
eigen-vector
multiple-selects
+
–
3
3 votes
2
2 answers
405
405 views
TIFR CSE 2025 | Part A | Question: 8
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...
Shubham Sharma 2
405
views
asked
Jun 16, 2025
Linear Algebra
tifr2025
linear-algebra
matrix
trace-of-matrix
expectation
+
–
0
0 votes
0
0 answers
206
206 views
TIFR Mathematics 2025 | Part A | Question: 17
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 $\operatorname{trace}(X)=0$....
Shubham Sharma 2
206
views
asked
Jun 16, 2025
Linear Algebra
tifrmaths2025
linear-algebra
matrix
trace-of-matrix
+
–
0
0 votes
0
0 answers
181
181 views
TIFR Mathematics 2025 | Part B | Question: 9
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...
Shubham Sharma 2
181
views
asked
Jun 16, 2025
Linear Algebra
tifrmaths2025
linear-algebra
vector-space
trace-of-matrix
true-false
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