If a linear operator T makes a vector zero, a product of linear operators containing T makes that vector zero. Why?
447
Minimal polynomial for T is a product of distinct linear factors
1475
In an incomplete inner product space, is a closed linear subspace equal to the orthogonal complement of its orthogonal complement?
152147
Why is a set of orthonormal vectors linearly independent?
52621
Why is $\det(A - \lambda I)$ zero?
83970
Proof of an elementary property of Projection Operators
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
42334
Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
6202
$V$ be a vector space , $T:V \to V$ be a linear operator , then is $\ker (T) \cap R(T) \cong R(T)/R(T^2) $?
131906
"An operator is hermitian". Implications?
91911
A linear operator between $C[0,1]$ and $C[0,1]$ defined as $Tf = f + \int f$; Show $T$ is an isomorphism
122562
Cross product term in linear regression why is it zero
1162
Why $\{\mathbf{0}\}$ has dimension zero?
43801
Why is $\operatorname{Div}\big(\operatorname{Curl} F\big) = 0$? Intuition?
52198
Why is every selfadjoint operator closed?
122951
If the $\det(A)=0$ why does the matrix $A$ have an eigenvector?
114250
If $V_0$ is the subspace of matrices of the form $C=AB-BA$ for some $A,B$ in a vector space $V$ then $V_0=\{A\in V|\operatorname{Trace} (A)=0\}$