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.
(34) | e₁₁ e₁₂ e₁₃ e₁₄ | = | 1 0 0 0 |
| e₂₁ e₂₂ e₂₃ e₂₄ | | 0 1 0 0 |
| e₃₁ e₃₂ e₃₃ e₃₄ | | 0 0 1 0 |
| e₄₁ e₄₂ e₄₃ e₄₄ | | 0 0 0 1 |
For a 4 × 4 series-matrix, Det A shall denote the determinant formed of
the 4 × 4 elements of the matrix. If det A ≠ 0, then corresponding to A
there is a reciprocal matrix, which we may denote by A⁻¹ so that A⁻¹A =
1.