The Matrix class represents a mathematical matrix. It provides methods for creating matrices, operating on them arithmetically and algebraically, and determining their mathematical properties (trace, rank, inverse, determinant).

Method Catalogue

To create a matrix:

• Matrix

• ::[]

• ::rows(rows, copy = true)

• ::columns

• ::build(row_count, #column_count, &block)

• ::diagonal

• ::scalar(n, value)

• ::identity

• ::unit

• Matrix.I(n)

• ::zero

• ::row_vector

• ::column_vector

To access Matrix elements/columns/rows/submatrices/properties:

• [](i, j)

• row_count (row_size)

• column_count (column_size)

• row(i)

• column(j)

• collect

• map

• each

• each_with_index

• find_index

• minor(*param)

Properties of a matrix:

• diagonal?

• empty?

• hermitian?

• lower_triangular?

• normal?

• orthogonal?

• permutation?

• real?

• regular?

• singular?

• square?

• symmetric?

• unitary?

• upper_triangular?

• zero?

Matrix arithmetic:

• #*(m)

• #+(m)

• #-(m)

• #/(m)

• inverse

• inv

• #**

Matrix functions:

• determinant

• det

• rank

• round

• trace

• tr

• transpose

• t

Matrix decompositions:

• eigen

• eigensystem

• lup

• lup_decomposition

Complex arithmetic:

• conj

• conjugate

• imag

• imaginary

• real

• rect

• rectangular

Conversion to other data types:

• coerce(other)

• row_vectors

• column_vectors

• to_a

String representations:

• to_s

• inspect