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In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. The elementary matrices generate the general linear group of invertible matrices. Left multiplication (pre-multiplication) by an elementary matrix represents elementary row operations, while right multiplication (post-multiplication) represents elementary column operations. The acronym "ERO" is commonly used for "elementary row operations". Elementary row operations are used in Gaussian elimination to reduce a matrix to row echelon form. They are also used in Gauss-Jordan elimination to further reduce the matrix to reduced row echelon form. ==Operations== There are three types of elementary matrices, which correspond to three types of row operations (respectively, column operations): ;Row switching: A row within the matrix can be switched with another row. : ;Row multiplication: Each element in a row can be multiplied by a non-zero constant. : ;Row addition: A row can be replaced by the sum of that row and a multiple of another row. : If ''E'' is an elementary matrix, as described below, to apply the elementary row operation to a matrix ''A'', one multiplies the elementary matrix on the left, ''E⋅A''. The elementary matrix for any row operation is obtained by executing the operation on the identity matrix. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Elementary matrix」の詳細全文を読む スポンサード リンク
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