What is the characteristic polynomial of a matrix?
Understand the Problem
The question is asking for the mathematical expression that defines the characteristic polynomial of a matrix, which is usually derived from the determinant of a matrix subtracted by a scalar multiple of the identity matrix. This polynomial is essential in linear algebra for finding the eigenvalues of the matrix.
Answer
det(A - λI)
The characteristic polynomial of a matrix A is given by det(A - λI), where λ is a scalar.
Answer for screen readers
The characteristic polynomial of a matrix A is given by det(A - λI), where λ is a scalar.
More Information
The characteristic polynomial is unique to a given square matrix and helps in finding the eigenvalues, as the roots of this polynomial are the eigenvalues of the matrix.
Tips
A common mistake is to incorrectly compute the determinant of (A - λI). Ensure each step in the matrix determinant calculation is precise.
Sources
- The Characteristic Polynomial - textbooks.math.gatech.edu
- Characteristic Polynomial - Definition, Formula and Examples - byjus.com
- Characteristic polynomial - Wikipedia - en.wikipedia.org
