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D. Matrix Algebra > Matrix Addition

Matrix Addition

The easiest matrix operation is addition. To add two matrices, you add their corresponding elements. This, of course, requires that your matrices have exactly the same number of rows and columns. Figure D-3 shows the addition of 2 matrices, each 3-by-2.

Addition of two 3 by 2 matrices
Figure D-3. Addition of two 3 by 2 matrices

We see that the translate transformation in SVG could be accomplished easily by matrix addition. For example, the matrix addition in Figure D-4 would implement transform="translate(7, 2)" for any point (x, y).

Simple method to translate coordinates
Figure D-4. Simple method to translate coordinates

The order in which you add matrices doesn’t matter. Technically, we say that matrix addition is commutative (A + B = B + A). It is also associative; given three matrices A, B, and C, (A + B) + C is the same as A + (B + C). There is such a thing as matrix subtraction; just subtract the corresponding elements of the two matrices. Just as with regular subtraction, matrix subtraction is not commutative.


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