Question

Decomposition of a surjective linear map

score 579 · Answer 1 · 2017-04-21 19:59:24

579

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Decomposition of a surjective linear map

Published on 21 Apr 2017 - 19:59

score 96 · Answer 2 · 2017-04-22 19:17:58

96

Views

Find three subspaces $W_1$, $W_2$ and $W_3$ of $k [X]$ such that $k[X]\cong W_1\oplus W_2\oplus W_3$

Published on 22 Apr 2017 - 19:17

score 191 · Answer 3 · 2026-02-23 06:24:24

191

Views

Homomorphic images of nth power of a division ring

Published on 23 Feb 2026 - 6:24

score 158 · Answer 4 · 2017-05-01 19:50:16

158

Views

How do you find the Orthogonal complement of U with respect to the standard dot product and what does it represent geometrically?

Published on 01 May 2017 - 19:50

score 981 · Answer 5 · 2017-05-05 16:14:25

981

Views

Direct sum seen as functor.

Published on 05 May 2017 - 16:14

score 275 · Answer 6 · 2026-02-23 20:37:30

275

Views

Finite sum & power series

Published on 23 Feb 2026 - 20:37

score 70 · Answer 7 · 2017-05-11 07:21:05

70

Views

$V = \sum_{i=1}^{n} \oplus U_i \Rightarrow {\rm dim}\ (V) = \sum_{i=1}^{n}{\rm dim}\ (U_i) $

Published on 11 May 2017 - 7:21

score 389 · Answer 8 · 2017-05-12 17:52:36

389

Views

Direct Sum: Span of Basis Vectors

Published on 12 May 2017 - 17:52

score 29 · Answer 9 · 2017-05-13 13:24:11

29

Views

Proving $f(T_1 \oplus T_2) = f(T_1) \oplus f(T_2)$ for $T = T_1 \oplus T_2$

Published on 13 May 2017 - 13:24

score 145 · Answer 10 · 2017-05-16 18:18:46

145

Views

Sum of two submodules of a module, each of which is a direct summand, is again a direct summand?

Published on 16 May 2017 - 18:18

score 860 · Answer 11 · 2017-05-18 10:55:13

860

Views

tangent space of cartesian product

Published on 18 May 2017 - 10:55

score 493 · Answer 12 · 2017-05-28 09:34:17

493

Views

Show a Kernel and Image of Direct Sum by Block Matrix

Published on 28 May 2017 - 9:34

score 170 · Answer 13 · 2017-05-30 08:59:34

170

Views

How to prove that $W=U_1 \oplus(U_2 \cap W)$ if $U_1 \subseteq W$, given that $V=U_1 \oplus U_2$ and $U_1,U_2,W$ are subspaces of $V$?

Published on 30 May 2017 - 8:59

score 82 · Answer 14 · 2017-05-30 11:20:58

82

Views

Give an example of $W \neq(U_1 \cap W) \oplus (U_2 \cap W)$ if $V=U_1 \oplus U_2$ and $U_1,U_2,W$ are the subspaces of $V$

Published on 30 May 2017 - 11:20

score 559 · Answer 15 · 2017-05-31 03:20:14

559

Views

Understanding direct sum and span proof

Published on 31 May 2017 - 3:20

List Question

Decomposition of a surjective linear map

Find three subspaces $W_1$, $W_2$ and $W_3$ of $k [X]$ such that $k[X]\cong W_1\oplus W_2\oplus W_3$

Homomorphic images of nth power of a division ring

How do you find the Orthogonal complement of U with respect to the standard dot product and what does it represent geometrically?

Direct sum seen as functor.

Finite sum & power series

$V = \sum_{i=1}^{n} \oplus U_i \Rightarrow {\rm dim}\ (V) = \sum_{i=1}^{n}{\rm dim}\ (U_i) $

Direct Sum: Span of Basis Vectors

Proving $f(T_1 \oplus T_2) = f(T_1) \oplus f(T_2)$ for $T = T_1 \oplus T_2$

Sum of two submodules of a module, each of which is a direct summand, is again a direct summand?

tangent space of cartesian product

Show a Kernel and Image of Direct Sum by Block Matrix

How to prove that $W=U_1 \oplus(U_2 \cap W)$ if $U_1 \subseteq W$, given that $V=U_1 \oplus U_2$ and $U_1,U_2,W$ are subspaces of $V$?

Give an example of $W \neq(U_1 \cap W) \oplus (U_2 \cap W)$ if $V=U_1 \oplus U_2$ and $U_1,U_2,W$ are the subspaces of $V$

Understanding direct sum and span proof

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