query: Prove that $\|x\|_A$ is a vector norm.
positive_passages.docid: 146405
positive_passages.text: Norm with symmetric positive definite matrix
negative_passages.docid: 102529
negative_passages.text: Prove that the set $\left\{ x, Ax, \dots, A^{k-1} x \right\}$ is linearly independent
negative_passages.docid: 134131
negative_passages.text: Squared norm of matrix equal to squared norm of its transpose
negative_passages.docid: 93511
negative_passages.text: Prove that $C^1([a,b])$ with the $C^1$- norm is a Banach Space
negative_passages.docid: 144112
negative_passages.text: Show that $c_0$ is a Banach space with the norm $\rVert \cdot \lVert_\infty$
negative_passages.docid: 83970
negative_passages.text: Proof of an elementary property of Projection Operators
negative_passages.docid: 97121
negative_passages.text: A question on subordinate matrix norm
negative_passages.docid: 51302
negative_passages.text: Show that the operator norm is submultiplicative
negative_passages.docid: 14448
negative_passages.text: Elementary proof that $|x|^p$ is convex.
negative_passages.docid: 49087
negative_passages.text: Show that a norm on an inner product space satisfies parallelogram law.
negative_passages.docid: 127248
negative_passages.text: Norm and unit sphere
negative_passages.docid: 60887
negative_passages.text: $d_A(x) = \inf_{a \in A} \|x-a\|$ is convex if and only if $A$ is convex
negative_passages.docid: 10383
negative_passages.text: The $ l^{\infty} $-norm is equal to the limit of the $ l^{p} $-norms.
negative_passages.docid: 51177
negative_passages.text: When are two norms equivalent on a Banach space?
negative_passages.docid: 122305
negative_passages.text: Proof of matrix norm property: submultiplicativity
negative_passages.docid: 106408
negative_passages.text: Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
negative_passages.docid: 110654
negative_passages.text: Vector Spaces and AC