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I am little confused about re-arranging matrix equations... So I know you cannot rearrange multiplication of matricies like you would normally with algebra as you cannot divide, but can you still do something like this when multiplication is not in the question?

T+Y = D
T = D-Y

Taylor Dale
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    Yes, addition is a commutative group operation on matrices, so it doesn't work any differently from ordinary addition for numbers. – Raskolnikov Apr 18 '13 at 12:07
  • Indeed the set of matrices forms a vector space over $\mathbb{C}$. – Tapu Apr 18 '13 at 12:10

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Yes, matrices form a vector field under addition and multiplication by scalars. It is sometimes useful to fold matrices into vectors, e.g., but stacking their columns into one tall column vectors. One can introduce the notions of norm and inner product in this way.

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