English Dictionary

Jordan block

名詞

(mathematics) A Jordan block over a ring R (whose identities are the zero 0 and one 1) is a matrix composed of 0 elements everywhere except for the diagonal, which is filled with a fixed element λ ∈ R, and the superdiagonal, which is composed of ones.

日本語の意味

（数学）ある環 R 上に定義される正方行列の一種で、対角成分が固定の値 λ で埋められ、その上対角線成分が 1、その他の成分が 0 になる行列。特に、ジョルダン標準形の構成要素として用いられる。

When studying the canonical form of a linear operator, we often consider a Jordan block to represent each elementary component, with λ on the diagonal and ones on the superdiagonal.

線形作用素の標準形を研究する際、各基本成分を表すために、対角にλが並び、その一つ上の副対角に1が並ぶ上三角行列をよく考える。

意味（1）

(mathematics) A Jordan block over a ring R (whose identities are the zero 0 and one 1) is a matrix composed of 0 elements everywhere except for the diagonal, which is filled with a fixed element λ ∈ R, and the superdiagonal, which is composed of ones.

Jordan blocks （ plural ）