Last Updated：2025/12/03

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(linear algebra) A square (n×n) matrix that has fewer than n linearly independent eigenvectors, and is therefore not diagonalisable.

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defective matrix

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Source Word

defective matrix

Noun

(linear algebra) A square (n×n) matrix that has fewer than n linearly independent eigenvectors, and is therefore not diagonalisable.

Japanese Meaning

正方行列であって、固有ベクトルの線形独立な数が行列の次数 n 未満であるため、対角化できない行列。

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Google Translation / DeepL Translation

独立な固有ベクトルが n 個未満の n×n の行列だったため、系は対角化できず、解くのがはるかに難しくなった。

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(linear algebra) A square (n×n) matrix that has fewer than n linearly independent eigenvectors, and is therefore not diagonalisable.

An n x n matrix A is a defective matrix if it has a defective eigenvalue.

Obviously, a Jordan block of dimension greater than 1, and a matrix whose Jordan canonical form has a Jordan block of dimension greater than 1, are defective matrices.

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defective matrices

（ plural ）

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defective matrix

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