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Prove uniqueness of solutions of different OLS matrix cases

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#linear-algebra #statistics #matrix-equations #matrix-rank #linear-regression
115
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rank of the matrix dependent on parameter

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#calculus #matrices #matrix-equations #matrix-rank
123
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Rank of the diagonal submatrices of full rank square matrix

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#linear-algebra #matrices #matrix-equations #matrix-rank
42
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If $A=B+C$ and $\operatorname{rank} A=2$, $\operatorname{rank} B=\operatorname{rank} C=1$, are $B$ and $C$ unique?

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#linear-algebra #matrices #matrix-rank
460
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Solving for matrix X (using the Moore-Penrose Pseudoinverse)

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#linear-algebra #matrices #systems-of-equations #matrix-rank #pseudoinverse
158
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Linear independence of matrix minors

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#linear-algebra #matrices #determinant #matrix-rank
283
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$\mathbb{R}^2, \mathbb{R}^3$ matrix/canonical basis

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#linear-algebra #matrices #linear-transformations #matrix-rank #change-of-basis
72
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SVD properties - what can we say about connections between different ranks of distortion?

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#matrices #matrix-rank #svd
153
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Algebra of endomorphisms with minimal polynomial of bounded rank

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#linear-algebra #abstract-algebra #matrices #representation-theory #matrix-rank
60
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Rank of a real matrix given the number of solutions for multiple systems

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#linear-algebra #matrices #matrix-rank
283
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How to describe the space of all $2 \times 2$ matrices of rank $1$?

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#linear-algebra #matrices #vector-spaces #determinant #matrix-rank
119
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Basis for a column space

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#linear-algebra #matrix-rank #hamel-basis
522
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rank of a matrix by linearly independent rows

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#linear-algebra #matrices #matrix-rank
39
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$rank(A) > rank(B) $ then $rank(f(A)) \geq rank(f(B)) $

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#matrices #matrix-rank
164
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Does a (square) full rank matrix have identical column and row spaces?

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#linear-algebra #matrices #matrix-rank #gaussian-elimination

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