The Principle of Relativity

by Albert Einstein; H. Minkowski

| b_{q 1} .......... b_{p r} |

where the number of horizontal rows of B, is equal to the number of vertical columns of A, then by AB, the product of the matrices A and B, will be denoted the matrix

C = | c₁₁ .......... c₁_r |

| |

| c_pr .......... c_{p p} |

where c_{h k} = a_{h 1} b₁_k + a_{h 2} b_{2 h} + ... a_{k s} b_{s k} + ... + a_{k q} b_{q h}

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 (AB)S = A(BS) 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 C = BA, we have Ċ = ḂĀ

3⁰. 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.