Let $T: V \rightarrow W $ be a linear mapping such that $T^2=T$, show that $V = M \oplus N$.
141191
Show that the direct sum of a kernel of a projection and its image create the originating vector space.
48990
Linear map $f:V\rightarrow V$ injective $\Longleftrightarrow$ surjective
24657
Let $T,S$ be linear transformations, $T:\mathbb R^4 \rightarrow \mathbb R^4$, such that $T^3+3T^2=4I, S=T^4+3T^3-4I$. Comment on S.
106408
Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
20879
Let $T:V→V$ be a linear transformation satisfying $T^2(v)=-v$ for all $v\in V$. How can we show that $n$ is even?
88857
Prove that Gauss map on M is surjective
23095
Prove that T is a linear transformation
34700
Proving that the matrix exponential map is surjective onto the general linear group
101467
Let $T:V\to V$ be a linear map, where $V$ is an inner product space. Given $T^2=\frac{T+T^*}{2}$, prove that $T$ is normal and that $T=T^2$.
114906
For $n \in \mathbb{N}$ and $W \leq \mathbb{F}^n$, there exists a homogeneous system of linear equations whose solution space is $W$
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
112231
Showing that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set
96458
Does $X_n \overset{L^2}{\rightarrow} X$ imply $X_n^2 \overset{L^1}{\rightarrow} X^2$?
104258
Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
80279
Show that $S + T$ and $aT$ are linear
62950
Use implicit function theorem to show $O(n)$ is a manifold
20467
Show that $(y_n)\in l^q$