dimension of a direct sum is the sum of the separate dimensions
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
74764
Dimension for a closed subspace of $C[0,1]$.
107520
Krull dimension of $\mathbb{C}[x_1, x_2, x_3, x_4]/\left$
114142
How to show that $\mathbb{R}^3$ is the direct sum of $W_1={\rm span}\{(1,1,1)\}$ and $W_2={\rm span}\{(1,0,0),(1,1,0)\}$?
132085
Minkowski sum and product of 2D-regions
74481
Distribution of scalar products of two random unit vectors in $D$ dimensions
6547
Given $3$-dimensional subspaces $V, W \subset \Bbb R^5$, there is a nonzero vector in $V \cap W$
37060
The Parallelogram Identity for an inner product space
85222
Direct sum of finitely-many non-abelian groups
95943
Dimension analysis of an integral
84871
Determining the dimension of span$\{AB-BA : A,B \in M_{n \times n}(\mathbb R) \}$
53364
dim$(V)$ = $n$, dim$(W)$ = $m$ $\implies$ dim($L(V,W)$) = $nm$
126136
Fundamental question about dimensional analysis
41347
The dimension of the intersection of two vector subspaces
7069
On the product of $\mathfrak c$-many separable spaces
133003
Prove about direct sum
123595
Representations of Direct Sum of Lie Algebras