Matrices
, Matrix Algebra
row vector 𝑣 = (𝑣1 , 𝑣2 , … , 𝑣𝑛 )
𝑣1
𝑣2
..
column vector 𝑣=
.
𝑣𝑛
, An m x n, or m by n, rectangular array
of numbers enclosed within brackets, and
arranged in m rows and n columns,
𝑎11 𝑎12 . . . 𝑎1𝑛
𝑎21 𝑎2𝟐 . . . 𝑎2𝑛
. . . . . .
. . . . . .
. . . . . .
𝑎𝑚1 𝑎𝑚2 . . . 𝑎𝑚𝑛
, And may be thought of as an ordered
set of m row vectors each of dimension n,
𝑢𝑖 = 𝑎𝑖1 , 𝑎𝑖2 , … , 𝑎𝑖𝑛 𝑖 = 1, 2, … . , 𝑚
or as an ordered set of n column vectors
each of dimension m.
𝑎1𝑗
𝑎2𝑗
..
𝑣𝑗 = 𝑗 = 1, 2, … , 𝑛
.
𝑎𝑚𝑗
, Matrix Algebra
row vector 𝑣 = (𝑣1 , 𝑣2 , … , 𝑣𝑛 )
𝑣1
𝑣2
..
column vector 𝑣=
.
𝑣𝑛
, An m x n, or m by n, rectangular array
of numbers enclosed within brackets, and
arranged in m rows and n columns,
𝑎11 𝑎12 . . . 𝑎1𝑛
𝑎21 𝑎2𝟐 . . . 𝑎2𝑛
. . . . . .
. . . . . .
. . . . . .
𝑎𝑚1 𝑎𝑚2 . . . 𝑎𝑚𝑛
, And may be thought of as an ordered
set of m row vectors each of dimension n,
𝑢𝑖 = 𝑎𝑖1 , 𝑎𝑖2 , … , 𝑎𝑖𝑛 𝑖 = 1, 2, … . , 𝑚
or as an ordered set of n column vectors
each of dimension m.
𝑎1𝑗
𝑎2𝑗
..
𝑣𝑗 = 𝑗 = 1, 2, … , 𝑛
.
𝑎𝑚𝑗
