characteristic root of a square matrix Synonyms
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characteristic root of a square matrix Meaning
Wordnet
characteristic root of a square matrix (n)
(mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant
characteristic root of a square matrix Sentence Examples
- The characteristic roots of a square matrix are also known as eigenvalues.
- Calculating the characteristic roots of a matrix involves solving the characteristic equation.
- The characteristic roots of a matrix provide insights into its diagonalizability and determinant.
- A square matrix with distinct characteristic roots is diagonalizable.
- The number of times a characteristic root repeats corresponds to its algebraic multiplicity.
- A square matrix is singular if and only if it has at least one characteristic root of zero.
- The characteristic roots of a symmetric matrix are always real.
- The characteristic roots of a skew-symmetric matrix are purely imaginary or zero.
- The characteristic roots of a square matrix determine its stability in dynamical systems.
- Eigenvalue decomposition involves finding the characteristic roots and corresponding eigenvectors of a square matrix.
FAQs About the word characteristic root of a square matrix
(mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant
No synonyms found.
No antonyms found.
The characteristic roots of a square matrix are also known as eigenvalues.
Calculating the characteristic roots of a matrix involves solving the characteristic equation.
The characteristic roots of a matrix provide insights into its diagonalizability and determinant.
A square matrix with distinct characteristic roots is diagonalizable.
