Question

Let $F$ be a field and let $V$ be the subspace of $F[X]$ consisting of all polynomials of degree at most $4$. Find a complement for $V$ in $F[X]$.

score 204 · Answer 1 · 2015-09-11 12:20:03

204

Views

Let $F$ be a field and let $V$ be the subspace of $F[X]$ consisting of all polynomials of degree at most $4$. Find a complement for $V$ in $F[X]$.

Published on 11 Sep 2015 - 12:20

score 1k · Answer 2 · 2015-09-16 21:38:55

1k

Views

How to show that a sum of subspaces can be made into a direct sum using subspaces which are subsets of each original subspace

Published on 16 Sep 2015 - 21:38

score 92 · Answer 3 · 2015-09-17 19:40:20

92

Views

Cyclic-Decomposition related proof

Published on 17 Sep 2015 - 19:40

score 127 · Answer 4 · 2026-03-28 07:50:57

127

Views

Does the tensor product operation distribute over the (external) direct sum?

Published on 28 Mar 2026 - 7:50

score 290 · Answer 5 · 2026-03-26 17:29:16

290

Views

Help with proving a set is a spanning set

Published on 26 Mar 2026 - 17:29

score 809 · Answer 6 · 2015-10-11 06:37:20

809

Views

Direct sum counterexample

Published on 11 Oct 2015 - 6:37

score 91 · Answer 7 · 2015-10-11 19:12:31

91

Views

Simultaneously diagonalize the regular representation of C2 (+) C2 (+) C2.

Published on 11 Oct 2015 - 19:12

score 584 · Answer 8 · 2015-10-18 02:39:20

584

Views

Dual group of the direct sum of abelian groups

Published on 18 Oct 2015 - 2:39

score 349 · Answer 9 · 2015-10-18 12:09:02

349

Views

Does $A\oplus \mathbb{Z}\cong B\oplus \mathbb{Z}$ imply $A\cong B$?

Published on 18 Oct 2015 - 12:09

score 70 · Answer 10 · 2015-10-19 08:31:13

Let $φ: V→V$ be a linear map with $φ \circ φ = \text{id}$. If $U = \{v \in V | φ(v) = v\}, W = \{ v \in V | φ(v) = -v\}$. Prove $ V \cong U \oplus W$

score 874 · Answer 11 · 2026-03-23 23:32:22

874

Views

If $T:V\to V$ linear and $N(V)+R(T)=V$ then $V=N(T)\oplus R(T)$

Published on 23 Mar 2026 - 23:32

score 518 · Answer 12 · 2026-03-16 00:03:28

518

Views

Free R-module as a direct sum of copies of R

Published on 16 Mar 2026 - 0:03

score 956 · Answer 13 · 2015-10-25 18:11:24

956

Views

Projection of a vector onto direct sum subspace

Published on 25 Oct 2015 - 18:11

score 158 · Answer 14 · 2015-10-26 06:41:10

158

Views

Question about equations involving sum of powers modulo a prime

Published on 26 Oct 2015 - 6:41

score 312 · Answer 15 · 2026-03-21 15:22:03

312

Views

Splitting $\mathbb Z_{pq}$ into direct sum with $\mathbb Z_p$

Published on 21 Mar 2026 - 15:22

List Question

Let $F$ be a field and let $V$ be the subspace of $F[X]$ consisting of all polynomials of degree at most $4$. Find a complement for $V$ in $F[X]$.

How to show that a sum of subspaces can be made into a direct sum using subspaces which are subsets of each original subspace

Cyclic-Decomposition related proof

Does the tensor product operation distribute over the (external) direct sum?

Help with proving a set is a spanning set

Direct sum counterexample

Simultaneously diagonalize the regular representation of C2 (+) C2 (+) C2.

Dual group of the direct sum of abelian groups

Does $A\oplus \mathbb{Z}\cong B\oplus \mathbb{Z}$ imply $A\cong B$?

Let $φ: V→V$ be a linear map with $φ \circ φ = \text{id}$. If $U = \{v \in V | φ(v) = v\}, W = \{ v \in V | φ(v) = -v\}$. Prove $ V \cong U \oplus W$

If $T:V\to V$ linear and $N(V)+R(T)=V$ then $V=N(T)\oplus R(T)$

Free R-module as a direct sum of copies of R

Projection of a vector onto direct sum subspace

Question about equations involving sum of powers modulo a prime

Splitting $\mathbb Z_{pq}$ into direct sum with $\mathbb Z_p$

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