The basis for the space of 2x2 matrices, denoted as M2,2, consists of four specific matrices: 1. <code>[1 0; 0 0]</code> 2. <code>[0 1; 0 0]</code> 3. <code>[0 0; 1 0]</code> 4. <code>[0 0; 0 1]</code>. These matrices are linearly independent and span the entire space of 2x2 matrices, which has a dimension of 4. The 2x2 identity matrix does not serve as a basis for this space as it cannot span all possible 2x2 matrices.
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math2010 said:Is the 2x2 identity matrix abasis for 2x2 matrices? Because it's linearly independent and spanning the space? Can anyone explain?
I disagree with what Cronxeh said. The space of 2x2 matrices has dimension 4, so cannot be spanned by two vectors, let alone two vectors in R2.math2010 said:Homework Statement
What is a basis for the space of 2 x 2 matrices.
The Attempt at a Solution
I don't understand how to this at all. Is the 2x2 identity matrix abasis for 2x2 matrices? Because it's linearly independent and spanning the space? Can anyone explain?