Question

Prove $V$ is a direct sum of the kernels of the factors of a polynomial annihilating a linear operator $T$.

score 69 · Answer 1 · 2022-08-16 08:51:20

69

Views

Prove $V$ is a direct sum of the kernels of the factors of a polynomial annihilating a linear operator $T$.

Published on 16 Aug 2022 - 8:51

score 68 · Answer 2 · 2022-08-17 08:32:53

68

Views

Direct sum of kernels of factors of a polynomial annihilating $A$.

Published on 17 Aug 2022 - 8:32

score 54 · Answer 3 · 2026-03-29 11:02:10

54

Views

If two direct sums of modules are isomorphic, when do we know that the components are isomorphic?

Published on 29 Mar 2026 - 11:02

score 225 · Answer 4 · 2022-08-20 12:13:28

225

Views

Topological direct sum of vector spaces

Published on 20 Aug 2022 - 12:13

score 154 · Answer 5 · 2026-03-28 06:15:49

154

Views

Direct sum of injections is injection, categorically

Published on 28 Mar 2026 - 6:15

score 86 · Answer 6 · 2022-09-09 19:16:25

86

Views

Why is the direct sum of two vector spaces a categorical coproduct?

Published on 09 Sep 2022 - 19:16

score 69 · Answer 7 · 2022-09-21 13:53:44

69

Views

Showing that the direct sum of pairwise orthogonal and closed vector subspaces is a closed subspace of a Hilbert space $H$

Published on 21 Sep 2022 - 13:53

score 252 · Answer 8 · 2022-09-26 02:46:20

252

Views

$M$ is isomorphic to the external direct sum, is not the internal direct sum of submodules.

Published on 26 Sep 2022 - 2:46

score 170 · Answer 9 · 2022-10-05 10:46:21

170

Views

Direct Sum Exercise

Published on 05 Oct 2022 - 10:46

score 132 · Answer 10 · 2022-10-13 15:29:22

132

Views

is there a case where the intersection of two distinct subspaces of a direct sum is not {0}.

Published on 13 Oct 2022 - 15:29

score 74 · Answer 11 · 2026-03-22 04:02:03

74

Views

An element both in $V_\mu$ and in $V_\overline{\mu}$ is zero?

Published on 22 Mar 2026 - 4:02

score 184 · Answer 12 · 2022-10-16 19:39:32

184

Views

An example when $(U^\perp)^\perp = U$ but $V\ne U\oplus U^\perp$?

Published on 16 Oct 2022 - 19:39

score 78 · Answer 13 · 2026-03-29 07:34:44

78

Views

Confusion about direct limit of vector spaces

Published on 29 Mar 2026 - 7:34

score 39 · Answer 14 · 2026-03-29 19:09:57

39

Views

Polynomial acting on Direct sums of matrices

Published on 29 Mar 2026 - 19:09

score 40 · Answer 15 · 2022-11-01 23:16:08

40

Views

A decomposition of a vector space using a nilpotent linear map

Published on 01 Nov 2022 - 23:16

List Question

Prove $V$ is a direct sum of the kernels of the factors of a polynomial annihilating a linear operator $T$.

Direct sum of kernels of factors of a polynomial annihilating $A$.

If two direct sums of modules are isomorphic, when do we know that the components are isomorphic?

Topological direct sum of vector spaces

Direct sum of injections is injection, categorically

Why is the direct sum of two vector spaces a categorical coproduct?

Showing that the direct sum of pairwise orthogonal and closed vector subspaces is a closed subspace of a Hilbert space $H$

$M$ is isomorphic to the external direct sum, is not the internal direct sum of submodules.

Direct Sum Exercise

is there a case where the intersection of two distinct subspaces of a direct sum is not {0}.

An element both in $V_\mu$ and in $V_\overline{\mu}$ is zero?

An example when $(U^\perp)^\perp = U$ but $V\ne U\oplus U^\perp$?

Confusion about direct limit of vector spaces

Polynomial acting on Direct sums of matrices

A decomposition of a vector space using a nilpotent linear map

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