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Recent questions tagged dimension

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subspace and dimension
Let $V$ be a subspace of $\mathbb{R}^{10}$. Suppose $A$ is a $10 \times 10$ matrix with real entries. Let $A^k(V) = \{A^k\mathbf{x} : \mathbf{x} \in V\}$ for $k \ge 1$ an...
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Research Scholarships Screening Test Saturday, January 19, 2013 Q. 3.5
Notation: \( \mathbb{R}^n \) (respectively, \( \mathbb{C}^n \)) denotes the \( n \)-dimensional Euclidean space over \( \mathbb{R} \) (respectively, over \( \mathbb{C} \)...
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Research Scholarships Screening Test Saturday, January 19, 2019 Q. 1.9
\( n \in \mathbb{N} \), \( n \geq 2 \). \( M_n(\mathbb{R}) \) (respectively, \( M_n(\mathbb{C}) \)) will denote the set of all \( n \times n \) matrices with entries fro...
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