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