Question

Characterizing an idempotent matrix

score 115 · Answer 1 · 2021-08-03 08:23:53

115

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Characterizing an idempotent matrix

Published on 03 Aug 2021 - 8:23

score 77 · Answer 2 · 2021-09-07 12:43:52

77

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Prove that $V=V_0\oplus V_1$ where $T(v_0)=0$ for all $v_0\in V_0$ and $T(v_1)=v_1$ for all $v_1\in V_1$, where $T$ is an idempotent linear trans.

Published on 07 Sep 2021 - 12:43

score 228 · Answer 3 · 2021-09-12 01:42:36

228

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Jordan decomposition of Idempotent matrix.

Published on 12 Sep 2021 - 1:42

score 190 · Answer 4 · 2021-09-20 07:11:48

190

Views

Prove: $\det(I+A) = 2^{\text{rank}(A)}$ if $A$ is a square idempotent matrix. Find $(I+A)^{-1}$ such that the expression doesn't have inverses.

Published on 20 Sep 2021 - 7:11

score 244 · Answer 5 · 2021-10-07 10:16:08

244

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Prove a matrix is idempotent using algebra

Published on 07 Oct 2021 - 10:16

score 55 · Answer 6 · 2021-10-10 18:51:20

55

Views

How can I prove that a specific symmetric matrix $P = I - \frac{uu^T}{u^T u}$ is idempotent?

Published on 10 Oct 2021 - 18:51

score 265 · Answer 7 · 2021-10-15 06:05:52

265

Views

Is $\ker T = \ker T^*$ for idempotent operators?

Published on 15 Oct 2021 - 6:05

score 72 · Answer 8 · 2021-10-22 16:32:37

72

Views

Show that set subset of matrice of X in $M_{n}(R)$ such that X is idempotent, symmetric and with Tr(X) =1 is a submanifold

Published on 22 Oct 2021 - 16:32

score 205 · Answer 9 · 2021-11-17 09:52:04

205

Views

Continuous function from $[0,1]$ to set of idempotent matrices in $M_2(\mathbb{R})$

Published on 17 Nov 2021 - 9:52

score 76 · Answer 10 · 2021-11-22 12:12:53

76

Views

If $\operatorname{Idem}B\rightarrow \operatorname{Idem}(B/mB)$ is surjective then $B$ is a product of local rings

Published on 22 Nov 2021 - 12:12

score 48 · Answer 11 · 2021-12-05 13:11:23

48

Views

If both $k$, $k+1$ are idempotents in $\mathbb{Z}_n$ and $k≠0$ then $n=2k$

Published on 05 Dec 2021 - 13:11

score 41 · Answer 12 · 2021-12-07 16:34:19

41

Views

Is centralizing all idempotents just once enough to make a ring abelian?

Published on 07 Dec 2021 - 16:34

score 39 · Answer 13 · 2021-12-08 10:20:05

39

Views

Checking primitivity of central idempotents: does it suffice to only consider central summands?

Published on 08 Dec 2021 - 10:20

score 150 · Answer 14 · 2026-03-27 20:30:49

150

Views

Idempotency and Fixed-point combinators

Published on 27 Mar 2026 - 20:30

score 48 · Answer 15 · 2022-01-23 22:55:29

48

Views

Unit ring non-trivial where every element is idempotent

Published on 23 Jan 2022 - 22:55

List Question

Characterizing an idempotent matrix

Prove that $V=V_0\oplus V_1$ where $T(v_0)=0$ for all $v_0\in V_0$ and $T(v_1)=v_1$ for all $v_1\in V_1$, where $T$ is an idempotent linear trans.

Jordan decomposition of Idempotent matrix.

Prove: $\det(I+A) = 2^{\text{rank}(A)}$ if $A$ is a square idempotent matrix. Find $(I+A)^{-1}$ such that the expression doesn't have inverses.

Prove a matrix is idempotent using algebra

How can I prove that a specific symmetric matrix $P = I - \frac{uu^T}{u^T u}$ is idempotent?

Is $\ker T = \ker T^*$ for idempotent operators?

Show that set subset of matrice of X in $M_{n}(R)$ such that X is idempotent, symmetric and with Tr(X) =1 is a submanifold

Continuous function from $[0,1]$ to set of idempotent matrices in $M_2(\mathbb{R})$

If $\operatorname{Idem}B\rightarrow \operatorname{Idem}(B/mB)$ is surjective then $B$ is a product of local rings

If both $k$, $k+1$ are idempotents in $\mathbb{Z}_n$ and $k≠0$ then $n=2k$

Is centralizing all idempotents just once enough to make a ring abelian?

Checking primitivity of central idempotents: does it suffice to only consider central summands?

Idempotency and Fixed-point combinators

Unit ring non-trivial where every element is idempotent

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