# The sum of matrices of the same kind

May 29th, 2015
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Sum of matrices -To add two matrices of the same kind, we simply add the corresponding elements. Sum properties- Consider the set S of all n x m matrices (n and m fixed) and A and B are in S. From the properties of real numbers it's

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The sum of matrices of the same kindSum of matricesTo add two matrices of the same kind, we simply add the corresponding elements. Sum propertiesConsider the set S of all n x m matrices (n and m fixed) and A and B are in S.From the properties of real numbers it's immediate that A + B is in S the addition of matrices is associative in S A + 0 = A = 0 + A with each A corresponds an opposite matrix -A A + B = B + A Scalar multiplicationDefinitionTo multiply a matrix with a real number, we multiply each element with this number. PropertiesConsider the set S of all n x m matrices (n and m fixed). A and B are in S; r and s are real numbers. It is not difficult to see that: r(A+B) = rA+rB (r+s)A = rA+sA (rs)A = r(sA) (rA)T = r. ATSums in mathBecause in the following, there is an intensive use of the properties of sums, the reader who is not familiar with these properties must read first Sums in math .Remark. In this html document, for convenience, we'll write the word sum instead of the sigma sign.Multiplication of a row matrix by a column matrixThis multiplication is only possible if the row matrix and the column matrix have the same number of elements. The result is a ordinary number ( 1 x 1 matrix).To multiply the row by the column, you have to multiply all the corresponding elements, then make the sum of the results.Example. [1][2 1 3]. [2] = [19] [5]Multiplication of two matrices A.BThis product is defined on

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