| _a₁₁_...................._a__{1 _q_} |
| |
| |
| |
| _a__{_p_ 1}..........._a__{_p_ _q_} |
arranged in _p_ horizontal rows, and _q_ vertical columns is called a
_p_ × _q_ series-matrix, and will be denoted by the letter A.
If all the quantities _a__{_h_ _k_} are multiplied by C, the resulting
matrix will be denoted by CA.
If the roles of the horizontal rows and vertical columns be
intercharged, we obtain a _q_ × _p_ series matrix, which will be known
as the transposed matrix of A, and will be denoted by Ā.
Ā = | _a₁₁_ ...................... _a__{_p_ 1} |
| |
| _a__{1 _q_} ............ _a__{_p_ _q_} |
If we have a second _p_ × _q_ series matrix B,
B = | _b₁₁_ ......................... _b₁__{_q_} |
| |
| _b__{_p_ 1} ............. b_{_p_ _q_} |
then A + B shall denote the _p_ × _q_ series matrix whose members are
_a__{_h_ _k_} + _b__{_h_ _k_}.