characteristic polynomial
The 'characteristic polynomial' is a fundamental concept in linear algebra, crucial for determining the eigenvalues of a square matrix.
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Definition
C1Linear Algebra
(technical, academic)A polynomial obtained by subtracting a scalar multiple of the identity matrix from a square matrix and calculating the determinant, used to find the matrix's eigenvalues.
Example
- To find the eigenvalues of the matrix, we first compute its characteristic polynomial.
- The roots of the characteristic polynomial are the eigenvalues of the matrix.
C1Mathematics
(technical, academic)A polynomial whose roots are the eigenvalues of a square matrix or linear transformation.
Example
- In solving the differential equation, we derived the characteristic polynomial to find its solutions.
- The characteristic polynomial provides insight into the properties of the matrix.
Similar
Terms that have similar or relatively close meanings to "characteristic polynomial":
characteristic functionminimal polynomialpolynomial basisprimitive polynomial