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A normed vector space is a pair (V, ‖·‖ ) where V is a vector space and ‖·‖ a norm on V.
We often omit p or ‖·‖ and just write V for a space if it is clear from the context what (semi) norm we are using.
In a more general sense, a vector norm can be taken to be any real-valued vector that satisfies these three properties. The properties 1. and 2. together imply that if and only if x = 0.
A useful variation of the triangle inequality is for any vectors x and y.
This also shows that a vector norm is a continuous function.
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Example of linear functional in dual space?
dual space W* of W can naturally identified with linear functionals
What is a linear square meter for concrete?
The question is nonsense. A linear square metre is like a square circle! Linear refers to length or distance in 1-dimensional space while a square metre is a measure of area in 2-dimensional space.
How much is 2900 square yards in linear feet?
Square yards are a measure of area, i.e. 2-dimensional space, and linear feet are a measure of...well, lines, i.e. 1-dimensional space. One cannot be computed into the other.
How do you compute norm on matlab?
using the function norm(A,x) where A is the matrix/vector that you have to compute the norm for and x can be 1,2,inf, or 'fro' to compute the 1-norm, 2-norm, infinite-norm and frobenius norm respectively.
What are the different kinds of linear equation?
There can be linear equations with 1, 2, ... variables. Each of these is different since an equation with n variables belongs to n-dimensional space.
