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I know that rank (A+B)<= rank(A)+rank(B) but why is rank(A+B)>=rank(A)-rank(B)?

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#matrices #matrix-rank
177
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Problem on characteristic polynomial and minimal polynomial

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#linear-algebra #matrix-rank #jordan-normal-form #minimal-polynomials
213
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A question on characteristic polynomial and minimal polynomial

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#linear-algebra #matrices #diagonalization #matrix-rank
315
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How do I expand a matrix in terms of a sum of simpler matrices?

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#matrices #matrix-decomposition #matrix-rank
442
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Full rank lifted system description of state-space (A,B,C,D)

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#linear-algebra #control-theory #matrix-rank
170
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Rank after appending a column to a Vandermonde matrix

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#linear-algebra #matrix-rank
58
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How would I answer the following question about the rank of a matrix?

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#linear-algebra #matrices #algebra-precalculus #matrix-rank
115
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proving rank(A-B) is a distance function and that an isometry f:M-->Z exists

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#proof-verification #metric-spaces #linear-transformations #matrix-rank
53
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Two diagonal matrices

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#matrices #matrix-equations #matrix-calculus #matrix-rank
3.2k
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If $A^2 = I$, then $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$

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#linear-algebra #matrices #matrix-equations #matrix-rank
56
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how to get the result of matrices

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#matrices #matrix-equations #matrix-decomposition #matrix-rank
57
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Echelon form of a matrix

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#matrix-rank
95
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Why do I get differnt row reduced echelon form?

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#matrix-rank
28
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Finding rank(a) as a varies

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#linear-algebra #matrices #determinant #matrix-rank
1.1k
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Show that the $\text{rank}(A)=$ number of pivot elements in $T$.

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#linear-algebra #matrices #solution-verification #matrix-rank

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