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rank of block triangular matrix with linear independence in sub-matrices

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61
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Relation between rank and determinant

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49
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n-rows submatrices of a Vandermonde matrix have full rank?

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58
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Block matrix rank inequality

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#linear-algebra #matrices #matrix-equations #matrix-rank
74
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System of equation solution using rank

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#linear-algebra #matrix-rank
96
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show $\text{rank}(AB)+\text{rank}(BC)\leq \text{rank}(B)+\text{rank}(ABC)$ for matrices $A$, $B$ and $C$

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191
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show $A^2=A \iff \text{rank}(A)+\text{rank}(A-I)=n$

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71
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For any $n$-by-$n$ complex matrix $M$, prove that rank$(M)$ + rank $(M − M^3)$ = rank$( M − M^2)$+ rank$(M + M^2)$

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86
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Finding determinant and rank of matrix $A$

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#linear-algebra #matrices #matrix-rank
122
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Show rank of a skew-symmetric matrix is always even

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60
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Write a symmetric matrix of rank $r$ as the sum of $r$ matrices, each having a rank of 1

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71
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Matrix product that preserves the rank

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#linear-algebra #matrices #matrix-decomposition #matrix-rank
40
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Connection between permutations and rank–nullity?

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#linear-algebra #permutations #linear-transformations #symmetric-groups #matrix-rank
68
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Ranks of block matrices implication

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#linear-algebra #matrix-rank #control-theory #systems-theory
61
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$X = [1_n \hspace{1mm} Z]$ with full column rank, then $(I_n - \frac{1}{n}J_n)Z$ is full-column rank

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#linear-algebra #problem-solving #matrix-rank

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