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Bases for column spaces

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#linear-algebra #matrices #vector-spaces #matrix-rank
207
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relation between rank of power of a singular matrix with the algebraic multiplicity of zero

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#eigenvalues-eigenvectors #matrix-rank
80
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How to determine the rank of the following general $\mathbb{R}$-linear transformation.

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#linear-algebra #matrices #linear-transformations #matrix-rank
823
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How to prove the dimension identity of subspace? i.e. $\dim(V_1) + \dim(V_2) = \dim(V_1 + V_2) + \dim(V_1 \cap V_2)$

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#linear-algebra #matrices #vector-spaces #matrix-rank
241
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How can I prove that $[T]_B$ is a reversible matrix?

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#linear-algebra #matrices #linear-transformations #matrix-rank
165
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can I have $\det(A+B)=0$ if $\det(A)=0$ and $\det(B) \neq 0$?

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#determinant #matrix-equations #matrix-rank
1.4k
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Let $A$ be a diagonalizable real matrix such as $A^3=A$. Prove that $\mbox{rank}(A) = \mbox{tr}(A^2)$

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#linear-algebra #matrices #diagonalization #matrix-rank
161
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Row permuation of a matrix for a non-zero diagonal

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#linear-algebra #matrix-rank
165
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Tensor rank as a first order formula

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#logic #first-order-logic #tensors #matrix-rank #tensor-rank
467
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Rank of Matrix , Intersection of 3 planes

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#linear-algebra #matrices #matrix-rank #plane-geometry
1.5k
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Rank of Matrix, and row of zero's

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#linear-algebra #matrices #systems-of-equations #matrix-rank
82
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Rank of the matrix and adjugate relation

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#linear-algebra #matrix-rank
72
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Rank of matrix - simple problem

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#linear-algebra #matrix-rank
1.9k
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Sum of two rank $1$ matrices with some property gives rank $2$ matrix

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#linear-algebra #matrices #vectors #matrix-rank #orthonormal
366
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Rank Nullity Theorem and a Complex of Vector Spaces

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#linear-algebra #abstract-algebra #vector-spaces #matrix-rank

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