Question

Understanding the definition of the direct sum of subspaces of a vector space

score 1k · Answer 1 · 2016-02-14 07:17:49

1k

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Understanding the definition of the direct sum of subspaces of a vector space

Published on 14 Feb 2016 - 7:17

score 180 · Answer 2 · 2026-03-26 19:05:16

180

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Find a subspace $U \subseteq \mathbb{R}^3$ such that $\mathbb{R}^3 \cong U \oplus W$

Published on 26 Mar 2026 - 19:05

score 275 · Answer 3 · 2016-02-17 22:51:16

275

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Show that $V = V_1 \oplus \dots \oplus V_m \Leftrightarrow B = B_1 \cup \dots \cup B_m$ is a basis of $V$.

Published on 17 Feb 2016 - 22:51

score 674 · Answer 4 · 2016-02-22 02:34:24

674

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Necessary and sufficient condition for a linear operator to be invertible

Published on 22 Feb 2016 - 2:34

score 106 · Answer 5 · 2016-02-23 23:04:13

106

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Uniqueness of complement of a vector subspace

Published on 23 Feb 2016 - 23:04

score 597 · Answer 6 · 2016-02-26 06:52:25

597

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Finite dimensional counterexample for the cancellation law of the direct sum of vector spaces

Published on 26 Feb 2016 - 6:52

score 131 · Answer 7 · 2016-03-02 03:58:44

131

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Show that if $G= G_1 \oplus G_2$, where $G_1$ and $G_2$ are cyclic of orders $m$ and $n$, then $m$ and $n$ are not uniquely determined by $G$.

Published on 02 Mar 2016 - 3:58

score 52 · Answer 8 · 2016-03-09 12:03:28

52

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Prove that $J \cap R(1 - e) \neq \{0\}$

Published on 09 Mar 2016 - 12:03

score 443 · Answer 9 · 2026-03-27 10:44:36

443

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Submodules of a product of simple modules

Published on 27 Mar 2026 - 10:44

score 161 · Answer 10 · 2016-03-12 15:46:47

161

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Find the direct summands of $\mathbb Z/ 36\mathbb Z$

Published on 12 Mar 2016 - 15:46

score 2.2k · Answer 11 · 2016-03-21 17:54:00

2.2k

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Direct sum $\mathbb{R} \oplus \mathbb{R}$ - isn't intersection non-zero?

Published on 21 Mar 2016 - 17:54

score 1.5k · Answer 12 · 2016-03-24 23:28:31

1.5k

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The characteristic of a direct sum of two rings

Published on 24 Mar 2016 - 23:28

score 491 · Answer 13 · 2016-04-18 02:47:23

491

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Vector Space external direct sum

Published on 18 Apr 2016 - 2:47

score 82 · Answer 14 · 2016-04-20 03:20:45

82

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Let $V=W_1\oplus W_2=U_1\oplus U_2$, if $W_1\subset U_1$ and $ W_2\subset U_2$ $\Rightarrow$ $W_1=U_1$ and $W_2=U_2$

Published on 20 Apr 2016 - 3:20

score 97 · Answer 15 · 2026-03-27 20:19:51

97

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sum of vector subspaces + subspace generated by ~

Published on 27 Mar 2026 - 20:19

List Question

Understanding the definition of the direct sum of subspaces of a vector space

Find a subspace $U \subseteq \mathbb{R}^3$ such that $\mathbb{R}^3 \cong U \oplus W$

Show that $V = V_1 \oplus \dots \oplus V_m \Leftrightarrow B = B_1 \cup \dots \cup B_m$ is a basis of $V$.

Necessary and sufficient condition for a linear operator to be invertible

Uniqueness of complement of a vector subspace

Finite dimensional counterexample for the cancellation law of the direct sum of vector spaces

Show that if $G= G_1 \oplus G_2$, where $G_1$ and $G_2$ are cyclic of orders $m$ and $n$, then $m$ and $n$ are not uniquely determined by $G$.

Prove that $J \cap R(1 - e) \neq \{0\}$

Submodules of a product of simple modules

Find the direct summands of $\mathbb Z/ 36\mathbb Z$

Direct sum $\mathbb{R} \oplus \mathbb{R}$ - isn't intersection non-zero?

The characteristic of a direct sum of two rings

Vector Space external direct sum

Let $V=W_1\oplus W_2=U_1\oplus U_2$, if $W_1\subset U_1$ and $ W_2\subset U_2$ $\Rightarrow$ $W_1=U_1$ and $W_2=U_2$

sum of vector subspaces + subspace generated by ~

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