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linalg::addRow

Linear combination of matrix rows

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Syntax

linalg::addRow(A, r1, r2, s)
linalg::addRow(A, r1, r2, s1, s2)

Description

linalg::addRow(A, r1, r2, s1) adds s1 times row r1 to row r2, in the matrix A.

linalg::addRow(A, r1, r2, s) returns a copy of the matrix A in which row r2 of A is replaced by srow(A, r1) + row(A, r2).

linalg::addRow(A, r1, r2, s1, s2) returns a copy of the matrix A in which row r2 of A is replaced by s1row(A, r1) + s2row(A, r2).

Examples

Example 1

The following defines a 3×3 matrix over the integers:

A := Dom::Matrix(Dom::Integer)( 
  [[1, 2, 3], [4, 5, 6], [7, 8, 9]] 
)

We replace the 2nd row by - row(A, 1) + row(A, 2), i.e., we subtract the first row from the second:

linalg::addRow(A, 1, 2, -1)

Example 2

The following defines a 2×3 matrix over the reals:

B := Dom::Matrix(Dom::Real)( 
  [[sin(2), 0, 1], [1, PI, 0]] 
)

If s is an expression that does not represent a real number then an error message is reported. The following tries to replace the 1st row by xrow(B, 2) + row(B, 1), where x is an identifier which cannot be converted to the component ring Dom::Real of B:

delete x: linalg::addRow(B, 2, 1, x)
Error: Cannot convert 'x'. [linalg::addRow]

Example 3

If symbolic expressions are involved, then one may define matrices over the component ring created by Dom::ExpressionField. The following example defines a matrix over this default component ring:

delete a11, a12, a21, a22, x:
C := matrix([[a11, a12], [a21, a22]])

We retry the input from the previous example:

linalg::addRow(C, 2, 1, x)

Parameters

A

An m×n matrix of a domain of category Cat::Matrix

r1, r2

The row indices: positive integers less or equal to m

s, s1, s2

Expressions that can be converted to the component ring of A

Return Values

Matrix of the same domain type as A.

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