Matrices in Sage

## Description

The basic Sage command to enter the matrix

(1)
\begin{align} A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix} \end{align}

is A = matrix([[1, 2, 3], [4, 5, 6]]).

## Sage Cell

#### Code

A = matrix([[1, 2, 3], [4, 5, 6]])
A


## Options

#### Option

The matrix $A$ is a $2 \times 3$ matrix with entries in the integers.

#### Code

A = matrix([[1, 2, 3], [4, 5, 6]])
A.parent()


#### Option

The matrix $A$ below has entires in the rationals, QQ. We may replace QQ with RR (the floating point real numbers) or CC (the floating point complex numbers).

#### Code

A = matrix([[1, 2, 3], [4, 5, 6]])
A.parent()


#### Option

The number of rows (2) and columns (3) can be entered.

#### Code

A = matrix(QQ, 2, 3, [[1, 2, 3], [4, 5, 6]])
A


#### Option

You can specify how many rows the matrix will have and provide one big grand list of entries, which will get chopped up, row by row, if you prefer.

#### Code

A = matrix(QQ, 2, [1, 2, 3, 4, 5, 6])
A


#### Option

The commands A.nrows() and A.ncols() will return the number of rows and columns of the matrix $A$, respectively.

#### Code

A = matrix(QQ, 2, 3, [[1,2,3],[4,5,6]])
A.nrows(), A.ncols()


#### Option

The command A.base_ring() will return the ring or field for the entries in the matrix $A$.

#### Code

A = matrix(RR, [[1, 2, 3], [4, 5, 6]])
A.base_ring()


#### Option

Rows in the matrix $A$ and numbered 0 to 1, while columns are numbered 0 to 2. The command A[i,j] returns the entry in the $i$th row and $j$th column of the matrix $A$ or 6.

#### Code

A = matrix([[1, 2, 3], [4, 5, 6]])
A[1,2]


## Tags

CC: math.la.i.mat

Primary Tags: Linear algebra: Matrices.

Secondary Tags: Matrices: Matrix basics.

None

## Attribute

Author: R. Beezer

Date: 24 Jul 2017 13:53

Submitted by: Tom Judson