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The rank of a linear combination of operators

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#linear-algebra #abstract-algebra #matrices #determinant #matrix-rank
59
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How to find the rank of this matrix?

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#matrices #matrix-rank
124
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Is any full rank feature matrix unitary? If so, why?

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#linear-algebra #matrices #matrix-rank #projection-matrices #unitary-matrices
414
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Find a linear combination of matrices that has rank 1

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#matrices #matrix-rank #rank-1-matrices
2.7k
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Show that the matrix $I-uu^T$ has rank $n-1$ where $u$ is a unit vector in $R^n$

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#linear-algebra #matrices #matrix-rank #symmetric-matrices #projection-matrices
619
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Proof of injectivity of dual map using rank-nullity theorem

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#linear-algebra #matrix-rank #dual-spaces
25
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Minimization under rank constraint of two matrices

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#matrices #optimization #matrix-rank
337
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Prove that the adjugate of $A$ is diagonalizable for every $A$ with the same properties

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#linear-algebra #matrices #diagonalization #matrix-rank
205
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Rank and Kernel of subspace where dot product = 0.

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#linear-algebra #linear-transformations #matrix-rank
27
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How to obtain a rank-5 solution to an optimization problem

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#optimization #matrix-rank #constraints
332
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Prove that $\dim \operatorname{Nul}(A^t)=0$ and hence that $A$ has rank $m.$

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#linear-algebra #matrices #vector-spaces #matrix-rank #transpose
254
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What is the rank of the product of two full rank matrices?

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#linear-algebra #matrices #linear-transformations #matrix-rank
664
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How to choose a basis for the kernel of a matrix?

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#linear-algebra #matrices #matrix-rank
251
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Does a matrix of rank $r$ always contain an invertible submatrix of size $r\times r$?

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#matrix-rank
151
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How to prove that if $A$ and $B$ are $n\times n$ matrices then $\operatorname{rank}(A) + \operatorname{rank}(B) \le \operatorname{rank}(AB) + n$

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#matrix-rank

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