Question

show that linear space is direct sum of two subspaces and find projections

score 125 · Answer 1 · 2026-03-26 14:20:51

125

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show that linear space is direct sum of two subspaces and find projections

Published on 26 Mar 2026 - 14:20

score 523 · Answer 2 · 2017-06-29 20:16:09

523

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Show that $V$ is the internal direct sum of $U$ and $W$

Published on 29 Jun 2017 - 20:16

score 57 · Answer 3 · 2026-03-29 18:36:23

57

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If $A \oplus_{\infty} B$ is isometric isomorphic to $C \oplus_{\infty}D,$ then $A \cong C$ and $B \cong D$ or $A \cong D$ and $B \cong C$?

Published on 29 Mar 2026 - 18:36

score 353 · Answer 4 · 2017-07-05 21:32:27

353

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Direct sum operation and endomorphisms

Published on 05 Jul 2017 - 21:32

score 1.7k · Answer 5 · 2017-07-12 06:15:52

1.7k

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Formal usage of direct sum in a set of functions

Published on 12 Jul 2017 - 6:15

score 4.5k · Answer 6 · 2017-07-15 22:57:48

4.5k

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Formal definition of direct sum of operators.

Published on 15 Jul 2017 - 22:57

score 595 · Answer 7 · 2017-07-16 01:31:36

595

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Example of Coproduct from Wikipedia

Published on 16 Jul 2017 - 1:31

score 220 · Answer 8 · 2026-03-27 18:28:05

220

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Is the definition of the canonical projection given wrong ? If so, is there any problem in my correction?

Published on 27 Mar 2026 - 18:28

score 529 · Answer 9 · 2017-07-23 09:45:58

529

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Intuition behind Theorem pertaining to Direct Sums

Published on 23 Jul 2017 - 9:45

score 1.5k · Answer 10 · 2026-03-26 11:03:40

1.5k

Views

Minimal polynomial of direct sum

Published on 26 Mar 2026 - 11:03

score 854 · Answer 11 · 2017-07-23 20:23:38

854

Views

Homomorphism and direct sum.

Published on 23 Jul 2017 - 20:23

score 75 · Answer 12 · 2026-03-27 18:27:44

75

Views

For $x\in E$ and $x = x_1 + x_2$, where $x_1 \in E_1$, shouldn't the distance vector of x from the subspace $E_1$ be unique?

Published on 27 Mar 2026 - 18:27

score 820 · Answer 13 · 2017-07-26 21:24:34

820

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The commutativity of direct sums and tensor products

Published on 26 Jul 2017 - 21:24

score 1.6k · Answer 14 · 2017-07-27 07:42:00

1.6k

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If V is a finite dimensional vector space, if $N(T) \cap R(T)$ = {0}, prove that V = $N(T)\oplus R(T)$

Published on 27 Jul 2017 - 7:42

score 368 · Answer 15 · 2026-03-27 03:43:03

368

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Generalization of $n$-th dimensional vector space isomorphic to $n$-th product of a field

Published on 27 Mar 2026 - 3:43

List Question

show that linear space is direct sum of two subspaces and find projections

Show that $V$ is the internal direct sum of $U$ and $W$

If $A \oplus_{\infty} B$ is isometric isomorphic to $C \oplus_{\infty}D,$ then $A \cong C$ and $B \cong D$ or $A \cong D$ and $B \cong C$?

Direct sum operation and endomorphisms

Formal usage of direct sum in a set of functions

Formal definition of direct sum of operators.

Example of Coproduct from Wikipedia

Is the definition of the canonical projection given wrong ? If so, is there any problem in my correction?

Intuition behind Theorem pertaining to Direct Sums

Minimal polynomial of direct sum

Homomorphism and direct sum.

For $x\in E$ and $x = x_1 + x_2$, where $x_1 \in E_1$, shouldn't the distance vector of x from the subspace $E_1$ be unique?

The commutativity of direct sums and tensor products

If V is a finite dimensional vector space, if $N(T) \cap R(T)$ = {0}, prove that V = $N(T)\oplus R(T)$

Generalization of $n$-th dimensional vector space isomorphic to $n$-th product of a field

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