an
matrix is a rectangular array of entries,
high and
wide. we denote by
the set of
matrices.
we use capital letters to denote matrices. usually our matrices will be arrays of numbers, real or complex, but matrices can be arrays of polynomials, or of more general functions; a matrix can even be an array of other matrices. a vector
is an
matrix; a number is a
matrix.
a matrix can be constructed over a specific finite/infinite set of numbers. for example
which is the set of integers, when we say a matrix is over a specific field of numbers we mean that the numbers in the matrix are limited to that field of numbers
consider this matrix over the field
, where all the numbers are integers
ld(random_matrix(ZZ,5,4))