defective matrix
defective matrix noun: a square (n×n) matrix that has fewer than n linearly independent eigenvectors, and is therefore not diagonalisable.
Noun
defective matrix (plural defective matrices)
- 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.1994, Sigal Ar, Jin-Yi Cai, Chapter 5: Reliable Benchmarks Using Numerical Stability, Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery... - Therefore, the sum of the geometric multiplicities of a defective matrix will be less than n.2007, Thomas S. Shores, Applied Linear Algebra and Matrix Analysis, Springer, page 261
- An n x n matrix A is a defective matrix if it has a defective eigenvalue.
Forms of defective matrix
| plural | defective matrices |
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Questions about defective matrix
- What does defective matrix mean?
- Defective matrix means a square (n×n) matrix that has fewer than n linearly independent eigenvectors, and is therefore not diagonalisable.
- What part of speech is defective matrix?
- Defective matrix is a noun.
- What is the plural of defective matrix?
- The plural of defective matrix is defective matrices.
Words near defective matrix in the dictionary
Source and license
Adapted from Wiktionary: defective matrix (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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