English Dictionary

echelon

IPA（発音記号）

/ˈɛʃ.ə.lɒn/

形容詞

比較不可

(linear algebra) Of a matrix: having undergone Gaussian elimination with the result that the leading coefficient or pivot (that is, the first nonzero number from the left) of a nonzero row is to the right of the pivot of the row above it, giving rise to a stepped appearance in the matrix.

日本語の意味

階段行列：ガウス消去法を施し、非ゼロ行の先頭の非ゼロ要素（ピボット）が、その直上の行の先頭の非ゼロ要素より右に位置するような行列の形態。

After performing Gaussian elimination, the augmented matrix was echelon, which allowed me to finish solving the system by back-substitution.

ガウスの消去を行った後、拡大係数行列は階段形になり、後退代入で連立方程式を解き終えることができた。

意味（1）

(linear algebra) Of a matrix: having undergone Gaussian elimination with the result that the leading coefficient or pivot (that is, the first nonzero number from the left) of a nonzero row is to the right of the pivot of the row above it, giving rise to a stepped appearance in the matrix.

An echelon matrix is a matrix, not necessarily square, with the following two properties: (i) There is at least one non-zero entry; rows consisting entirely of zeros, if any, lie below rows with at least one non-zero entry. (ii) In each non-zero row after the first, the left-most non-zero entry lies to the right of the left-most non-zero entry in the preceding row. […] In each of the non-zero rows of an echelon matrix, the left-most non-zero entry is called the pivot, […]