Transformation To Row Echelon Form
By means of a finite sequence of elementary row operations, called Gaussian elimination, any matrix can be transformed to row echelon form. Since elementary row operations preserve the row space of the matrix, the row space of the row echelon form is the same as that of the original matrix.
The resulting echelon form is not unique; for example, any multiple of a matrix in echelon form is also in echelon form. However, it is the case that every matrix has a unique reduced row echelon form. This means that the nonzero rows of the reduced row echelon form are the unique reduced row echelon generating set for the row space of the original matrix.
Read more about this topic: Row Echelon Form
Famous quotes containing the words row and/or form:
“And, indeed, is there not something holy about a great kitchen?... The scoured gleam of row upon row of metal vessels dangling from hooks or reposing on their shelves till needed with the air of so many chalices waiting for the celebration of the sacrament of food. And the range like an altar, yes, before which my mother bowed in perpetual homage, a fringe of sweat upon her upper lip and the fire glowing in her cheeks.”
—Angela Carter (1940–1992)
“In every form of womanly love something of motherly love also comes to light.”
—Friedrich Nietzsche (1844–1900)