Matrix

Matrix()

A matrix with rational polynomial coefficients.

Methods

Name	Description
augment	Augment the matrix with another matrix, e.g. create [A B] from matrix A and B.
content	Get the content, i.e., the GCD of the coefficients.
det	Return the determinant of the matrix.
eye	Create a new matrix with the scalars diag on the main diagonal and zeroes elsewhere.
format	Convert the matrix into a human-readable string, with tunable settings.
from_linear	Create a new matrix from a 1-dimensional vector of scalars.
from_nested	Create a new matrix from a 2-dimensional vector of scalars.
identity	Create a new square matrix with nrows rows and ones on the main diagonal and zeroes elsewhere.
inv	Return the inverse of the matrix, if it exists.
is_diagonal	Return true iff every non- main diagonal entry in the matrix is zero.
is_zero	Return true iff every entry in the matrix is zero.
map	Apply a function f to every entry of the matrix.
ncols	Get the number of columns in the matrix.
nrows	Get the number of rows in the matrix.
primitive_part	Construct the same matrix, but with the content removed.
row_reduce	Row-reduce the first max_col columns of the matrix in-place using Gaussian elimination and return the rank.
solve	Solve A * x = b for x, where A is the current matrix.
solve_any	Solve A * x = b for x, where A is the current matrix and return any solution if the
split_col	Split the matrix into two matrices at column col.
to_latex	Convert the matrix into a LaTeX string.
transpose	Return the transpose of the matrix.
vec	Create a new column vector from a list of scalars.

augment

Matrix.augment(b)

Augment the matrix with another matrix, e.g. create [A B] from matrix A and B.

Returns an error when the matrices do not have the same number of rows.

content

Matrix.content()

Get the content, i.e., the GCD of the coefficients.

det

Matrix.det()

Return the determinant of the matrix.

eye

Matrix.eye(diag)

Create a new matrix with the scalars diag on the main diagonal and zeroes elsewhere.

format

Matrix.format(
    pretty_matrix=True,
    number_thousands_separator=None,
    multiplication_operator='*',
    double_star_for_exponentiation=False,
    square_brackets_for_function=False,
    num_exp_as_superscript=True,
    latex=False,
    precision=None,
)

Convert the matrix into a human-readable string, with tunable settings.

from_linear

Matrix.from_linear(nrows, ncols, entries)

Create a new matrix from a 1-dimensional vector of scalars.

from_nested

Matrix.from_nested(entries)

Create a new matrix from a 2-dimensional vector of scalars.

identity

Matrix.identity(nrows)

Create a new square matrix with nrows rows and ones on the main diagonal and zeroes elsewhere.

inv

Matrix.inv()

Return the inverse of the matrix, if it exists.

is_diagonal

Matrix.is_diagonal()

Return true iff every non- main diagonal entry in the matrix is zero.

is_zero

Matrix.is_zero()

Return true iff every entry in the matrix is zero.

map

Matrix.map(f)

Apply a function f to every entry of the matrix.

ncols

Matrix.ncols()

Get the number of columns in the matrix.

nrows

Matrix.nrows()

Get the number of rows in the matrix.

primitive_part

Matrix.primitive_part()

Construct the same matrix, but with the content removed.

row_reduce

Matrix.row_reduce(max_col)

Row-reduce the first max_col columns of the matrix in-place using Gaussian elimination and return the rank.

solve

Matrix.solve(b)

Solve A * x = b for x, where A is the current matrix.

solve_any

Matrix.solve_any(b)

Solve A * x = b for x, where A is the current matrix and return any solution if the system is underdetermined.

split_col

Matrix.split_col(col)

Split the matrix into two matrices at column col.

to_latex

Matrix.to_latex()

Convert the matrix into a LaTeX string.

transpose

Matrix.transpose()

Return the transpose of the matrix.

vec

Matrix.vec(entries)

Create a new column vector from a list of scalars.