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Matrix operations
Matrix Addition and Subtraction
If you have two matrices with the same dimensions (the same number of rows and columns), you can add them together. The result is a third matrix with the same number of rows and columns of the original two, but with the original matrix elements added together as follows:| ( |
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In this case I've used numbered symbols instead of actual numbers to make the procedure as clear as possible (the symbols are numbered with subscripts according to row and column number).
Basically, you take the number in row 1, column 1 of the first matrix, add it to the number in row 1, column 1 of the second matrix, and the result goes in row 1 column 1 of the answer. Then repeat for row 1, column 2.... and so on for each element in the matrix (each number in a matrix is called an element of that matrix).
As for subtracting one matrix for another, this is identical to addition except that you subtract the matrix elements instead of adding them.
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Again, both matrices must have the same number of rows and the same number of columns; otherwise the idea of subtracting one from the other simply doesn't make sense.
Multiplication of a matrix by a scalar
You can multiply any matrix by a scalar (like, for example, the number -5.1). Basically, this is equivalent to multiplying every element in the matrix by that scalar. For example, here I'll multiply a matrix by -10:| -10 | ( |
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Note that multiplying a matrix by a scalar is not the same as real matrix multiplication - multiplication of one matrix by another - rather it's just a kind of special case that applies to scalars.
Multiplication of a matrix by another matrix
You can multiply one matrix by another as long as the first matrix has the same number of columns as the number of rows in the second matrix. The procedure is a little more complicated than you might expect, and it takes a bit of getting used to; but the procedure is as follows:coming soon...
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