Prove that the norm of a linear transformation satisfies the inequality $\|Tx\| \leq M\|x\|$ for all $x$.
4498
Proof that $\|fx\| \leq \|f\|\cdot\|x\|$
154226
Upper bound for norm of Hilbert space operator
131596
Symmetric Inequality in $\mathbb{R}$
149997
Convolution operator has norm 1 with respect to $L^2$ norm
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
75059
Let $T:\mathbb{R}^n\to \mathbb{R}^n$ be a linear transformation...
103806
How to prove triangle inequality for $p$-norm?
139692
Proof of inequality using AM-GM inequality
132869
Show that any bounded linear functional on a normed linear space is continuous
90345
If $\lVert x\rVert=\lVert y \rVert$, prove that exists a unitary transformation such as $Tx=y$
10483
Prove Sylvester rank inequality: $\text{rank}(AB)\ge\text{rank}(A)+\text{rank}(B)-n$
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$
38850
How to show Von Neumann Trace inequality $ \text{Tr}(AB) \leq \sum_{i=1}^n \sigma_{A,i}\sigma_{B,i} $?
91662
Proof for triangle inequality for vectors
67058
Prove that $\text{rank}(X^TX)=\text{rank}(X)$
95677
Linear Matrix Inequality of a matrix $T$ with $\| T \|_2 < \rho$
126165
Prove $|\arctan x - \arctan y|\leq |x-y|$