Question

How to prove: if $AB=I$ then $\mathrm{rank}(A)=\mathrm{rank}(B)$ and if $AB=0$ then $\mathrm{rank}(A)+\mathrm{rank}(B)\le n$

score 944 · Answer 1 · 2026-04-16 14:10:13

944

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How to prove: if $AB=I$ then $\mathrm{rank}(A)=\mathrm{rank}(B)$ and if $AB=0$ then $\mathrm{rank}(A)+\mathrm{rank}(B)\le n$

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score 334 · Answer 2 · 2026-04-14 09:32:05

334

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623

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List Question

How to prove: if $AB=I$ then $\mathrm{rank}(A)=\mathrm{rank}(B)$ and if $AB=0$ then $\mathrm{rank}(A)+\mathrm{rank}(B)\le n$

Calculate the distance between x and y using inner product

Activating a perceptron with the step function

Orthogonal Projection of plane onto a line

Bases de una matriz

Determine eigenvalues and eigenvectors of a linear map

Given points P,Q, how do I prove (P+Q)/2 lies on the line PQ using vector geometry

Linear operators, matrices, kernels

What is $\mathbb{F}^{2, 2}$?

Can a vector space have more than one definition of an inner product?

Cost of Gaussian Elimination

Clarification on rules regarding division of two equations

Show that the given linear system has this specific solution if $\det \neq 0$

Center of shortest connection between two lines in 3D

If $ Ax=b $ has solution what about $ y $ in $ A^Ty=0 $

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