MAT223H1 Chapter Notes - Chapter 3.2: Matrix Addition, Diagonal Matrix, Block Matrix

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In this section we study the algebra of matrices, that is the. Arithmetic operations that can be performed over matri- ces and their properties. Although there are some similarities with real number op- erations, there are several important differences that we will point out as they appear. Let a be an n k matrix and b a k m matrix. Then the product ab is an n m matrix given by. , bm are the m columns of matrix b. This is a departure from the implementation of matrices addition and scalar multiplication. For those cases, opera- tions were performed element by element. The reason behind this de nition comes from the role that matrices play in linear transformations. S : rm rk (cid:55) s(x) = bx. T : rk rn (cid:55) t (y) = ay x y (3a) (3b) Nota the the existence of a and b is guaranteed by the fact that they come from linear transformations.

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