then by AB, the product of the matrices A and B, will be denoted the matrix
these elements being formed by combination of the horizontal rows of A with the vertical columns of B. For such a point, the associative law holds, where S is a third matrix which has got as many horizontal rows as B (or AB) has got vertical columns.
For the transposed matrix of , we have .
3°. We shall have principally to deal with matrices with at most four vertical columns and for horizontal rows.
As a unit matrix (in equations they will be known for the sake of shortness as the matrix 1) will be denoted the following matrix (4 ✕ 4 series) with the elements.
For a 4✕4 series-matrix, Det A shall denote the determinant formed of the 4✕4 elements of the matrix. If , then corresponding to A there is a reciprocal matrix, which we may denote by so that