Linear Algebra: Prove the orthogonal complement of the row space of A is {0} implies Ax = 0 has only the trivial solution
48579
How to find the orthogonal complement of a subspace?
33611
necessary and sufficient condition for trivial kernel of a matrix over a commutative ring
146984
Prove: Full Rank and a solution os linear system
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
120867
How prove this two symmetric matrices $AB=0$
113326
Proving orthogonality of vectors in a complex vector space
33448
Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
52928
If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$
69474
Orthogonal projections with $\sum P_i =I$, proving that $i\ne j \Rightarrow  P_{j}P_{i}=0$
69497
Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
130498
Linear algebra proof regarding matrices
122213
Proving that if $\langle Ax,x\rangle =0$ for every $x$, then $A$ is the zero operator
121987
Direct proof that nilpotent matrix has zero trace
138025
How to show the solution of $\dot{x} = Ax $ is an invariant subspace?
137920
Proving an equation with invertible matrices
35625
Direct sum of orthogonal subspaces