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Rank of a bijective function and bijectivity of a composition

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#linear-algebra #matrix-rank
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Conic hull of outer products

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#linear-algebra #matrices #convex-optimization #matrix-rank #positive-semidefinite
133
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Prove that if $\mathrm{rank}(A-I_n)=p$ and $\mathrm{rank}(B-I_n)=q$, then $\mathrm{rank}(AB-I_n)\leq p+q$

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Problem on the dimension of a linear space

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Determine whether A is diagonalizable using these three steps.

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#linear-algebra #eigenvalues-eigenvectors #matrix-rank
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Rank(AB) and Rank(BA)?

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Ranks of a matrix and determinants of its minors

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#linear-algebra #matrices #determinant #matrix-rank
119
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Give the following linear transformation find values of parameter

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29
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On Rank of matrices

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#linear-algebra #matrix-rank
272
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Probability measure of rank-$r$ matrices

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#matrices #measure-theory #matrix-rank
805
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Linear transformation to higher dimensional space.

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#linear-algebra #matrices #matrix-equations #linear-transformations #matrix-rank
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At least one diagonal element of any real symmetric matrix of rank $1$ is non-zero ?

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#matrices #matrix-rank
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If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$

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#matrices #inequality #matrix-rank
100
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Generation of rank-$2$ matrices from a dictionary of rank-$1$ matrices

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106
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Complex square matrices, proving there exists x,y in C^n such that A=xy*

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