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Vector Matrix vs Matrix Norms

Hey guys, I have a question regarding a question of an assignment I have, and I'll describe my attempt at a solutionAttachment 23459So I figured it should be pretty easy. I only need to prove the following three conditions for ||x|| to be a vector norm1.||x||>= 0 , for x is in R^{n} and ||x|| = 0 iff x=02. ||ax|| = |a| * ||x|| for x is in R^{n }and a is in R. ||x + y||

edit: "a is in R"

Re: Vector Matrix vs Matrix Norms

The matrix norm of a matrix, and the function defined here of vector x, is a **number**. What number is it for this x?

Re: Vector Matrix vs Matrix Norms

Isn't the vector norm represented by

||x||_{p }= (sum from k=1 to n, |x_{k}|)^{1/p }Is this the number you're referring to?

I apologize for my lack of latex coding. I've been trying to use it but have been failing miserably.