(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let M1 = [1 1] and M2 = [-3 -2]

________[1 -1]_________[ 1 2]

Consider the inner product <A,B> = trace(transpose(A)B) in the vector space R2x2 of 2x2 matrices. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R2x2 spanned by the matrices M1 and M2.

3. The attempt at a solution

So the inner product of the 2 matrices is <M1,M2> which is [-2 0]

__________________________________________________[-4 -4]

if I calculated it right which I think I did. But I don't what that has to do with Gram-Schmidt or how it relates to orthonormal bases for R2x2. And I know how to use Gram-Schmidt on individual vectors but not on a whole matrix so I'm pretty stuck.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Orthonormal basis spanned by 2 matrices

**Physics Forums | Science Articles, Homework Help, Discussion**