List questions from direct-sum

Published on 03 Aug 2016 - 18:50

2.1k

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Making a matrix block diagonal by linear transformation

Published on 05 Aug 2016 - 14:54

90

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Generalizing the formula for dim$(U+W)$

Published on 11 Aug 2016 - 10:54

31

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Find subspace $T$ such that $\mathbb{M}_{2\times 3}^{\mathbb{R}}=W\oplus T$

Published on 17 Aug 2016 - 14:38

1.4k

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Prove or give a counterexample: $V=\text{null}T+\text{range}T$

Published on 18 Aug 2016 - 0:16

846

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Why is cohomology the direct product of the $H^n$?

Published on 25 Mar 2026 - 22:41

1.7k

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Show that $\mathbb R^n$ is the direct sum of the subspaces $W_1$ and $W_2$

Published on 28 Aug 2016 - 15:59

2.7k

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Proof for $\mathbb{R}^{3}$ being the direct sum of two subspaces

Published on 29 Aug 2016 - 1:52

750

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Proof for basis of subspaces in direct sum being basis of its result

Published on 30 Aug 2016 - 12:22

999

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If $U_1, U_2, W$ are subspaces of $V$ such that $U_1 + W = U_2 + W$ then $U_1 = U_2$?

Published on 08 Sep 2016 - 1:20

176

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Why $G=H\times K$ implies $G=H\vee K$?

Published on 26 Mar 2026 - 17:36

110

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Changing perspective from external to internal direct product...

Published on 26 Mar 2026 - 17:35

474

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What is the purpose of direct sums in linear algebra?

Published on 18 Sep 2016 - 6:09

7.2k

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The direct sum of a rank and null space

Published on 24 Sep 2016 - 5:24

16

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From $M=\oplus_{i=1}^{n}S_i$ follows $pM=\oplus_{i=1}^{n}pS_i$?

Published on 10 Mar 2026 - 11:39

List Question

Direct sum $A\oplus B=\{v_2,v_3\}\oplus \{v_1,v_4\}$

Making a matrix block diagonal by linear transformation

Generalizing the formula for dim$(U+W)$

Find subspace $T$ such that $\mathbb{M}_{2\times 3}^{\mathbb{R}}=W\oplus T$

Prove or give a counterexample: $V=\text{null}T+\text{range}T$

Why is cohomology the direct product of the $H^n$?

Show that $\mathbb R^n$ is the direct sum of the subspaces $W_1$ and $W_2$

Proof for $\mathbb{R}^{3}$ being the direct sum of two subspaces

Proof for basis of subspaces in direct sum being basis of its result

If $U_1, U_2, W$ are subspaces of $V$ such that $U_1 + W = U_2 + W$ then $U_1 = U_2$?

Why $G=H\times K$ implies $G=H\vee K$?

Changing perspective from external to internal direct product...

What is the purpose of direct sums in linear algebra?

The direct sum of a rank and null space

From $M=\oplus_{i=1}^{n}S_i$ follows $pM=\oplus_{i=1}^{n}pS_i$?

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