ns are considered on a vector space. In this expository article, we explain why one would want to study different k. nds of norms on a real vector space. We then focus on the problem of how to identify …

In order to define how close two vectors or two matrices are, and in order to define the convergence of sequences of vectors or matrices, we can use the notion of a norm.

Norms generalize the notion of length from Euclidean space. A norm on a vector space V is a function k k : V ! R that satis es. for all u; v 2 V and all 2 F. A vector space endowed with a norm is called a …

Intended for new graduate students whose experience as undergraduates may have prepared them inadequately to apply norms to numerical error-analyses and to proofs of convergence, this tutorial …

January 18, 2019 In class we've used the `2-norm and the `1-norm as a measure of the length of a vector, and the concept of norm generalizes this idea. In particular, we say that a function f is a norm …

Definition matrix norm on Rn×n is a real-valued function ∥ · ∥ satisfying for all matrices A, B ∈ Rn×n and for all α ∈ R:

Frobenius squared all the |aij|2 and added; his norm is the square root. This treats A like a long vector with n2 components: sometimes kAkF useful, but not the choice here. I prefer to start with a vector …