nLab row operation

Contents

Idea

A row operation on a rectangular matrix with elements in a ring is an operation of replacing it with another matrix of the same dimensions which is of one of the following types

  • interchanging of two rows of the matrix

  • rescaling one row by multiplying it with a nonzero element

  • adding a multiple of one row to some other row.

Similarly, a column operation is either interchanging two columns, rescaling one column by multiplying it with a nonzero element or adding a multiple of one column to some other column.

Properties

Each row operation can be achieved by multiplying the matrix from the left by an elementary matrix.

If the ground ring is a field then each row operation is invertible.

category: algebra

Last revised on May 21, 2024 at 13:13:11. See the history of this page for a list of all contributions to it.