8 сент. 2013 г. · I've been searching for the definition of the submultiplicative (I think it has multiple names from what I've seen) property in proof form. Some ...

25 февр. 2016 г. · The given norm on V "induces" a norm on L(V), as described in the following. Inducing means that this norm can be defined without providing additional data.

24 сент. 2014 г. · Suppose |y|=1 is such that |A|=|Ay|. Then x=Ay/|A| also has norm 1 so it follows that |A−1|≥|A−1x|=|A−1Ay/|A||=|y||A|=1|A|=|A|−1.

6 апр. 2016 г. · I am struggling with following proof, could you give me some hint or some information which would help me in proving following inequality?

9 февр. 2015 г. · The matrix p-norm is the operator norm: ‖A‖p=maxx≠0‖Ax‖p‖x‖p. The fact that ‖A‖2=ρ(A∗A)and‖A‖∞=maxi∑j|aij|. is just the consequence of (1).

28 июл. 2013 г. · Proof of matrix norm property: submultiplicativity · 0 · Sketch unit ... State matrix norm (respect to Matrix) with matrix norm (respect to ...

1 окт. 2012 г. · proving matrix norm properties [closed] · 1. What are your definitions of B>>A and |Am|? · |Am|. is a matrix sequence >>means majorizes · I ...

4 янв. 2014 г. · Remember the vector norm have 3 properties just like matrix norm. So to prove ||A||=0 if and only if A=0, you refer to the fact that Ax=0 ...

8 сент. 2019 г. · 2 Answers. If A is the identity matrix, then Ix=x for all x∈V the associated vector space. Hence ‖Ix‖=1 for all x such that ‖x‖=1.

23 сент. 2015 г. · Mathematicians might phrase this question by asking how to show that all matrix norms, defined by ‖A‖=max(‖Ax‖/‖x‖), are actually norms, ...