List questions from idempotents | MathQa

Let A be a square matrix of order n. Prove that if $A^2 = A$, then $\operatorname{rank}(A) + \operatorname{rank}(I - A) = n$.

Published on 12 Jan 2025 - 23:35

$\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$ for $A$ idempotent matrix

Published on 02 Jan 2025 - 6:20

Finding (orthogonal) idempotents in a quotient of a polynomial ring

Published on 12 Jan 2025 - 10:05

Let $A ∈ M_{n×n}(\mathbb{R})$ differ from $I$ and $O$. If $A$ is idempotent, show that its Jordan canonical form is a diagonal matrix.

Published on 12 Jan 2025 - 23:33

Does inverse image of idempotent element contain an idempotent element?

Published on 12 Jan 2025 - 10:05

Proving that if $AB=A$ and $BA=B$, then both matrices are idempotent

Published on 12 Jan 2025 - 10:05

Prove $a,b\in R$ are idempotent iff $ab=0$.

Published on 12 Jan 2025 - 10:05

Find scalars that result in an idempotent matrix

Published on 12 Jan 2025 - 10:05

S an inverse semigroup with semilattice of idempotents E and $\sigma$ the minimum group congruence on S.

Published on 12 Jan 2025 - 10:05

Nonminimal idempotents

Published on 12 Jan 2025 - 17:36