Discover the characteristic polynomial of a matrix effortlessly with our Characteristic Polynomial Calculator. This powerful online tool helps you find the polynomial P(λ) = det(A - λI), which is fundamental for understanding a matrix's eigenvalues and eigenvectors. Perfect for students, researchers, and professionals in linear algebra.
Formula:
The characteristic polynomial, P(λ), of a square matrix A is defined by the formula:
P(λ) = det(A - λI)
Where:
Ais the given square matrix.λ(lambda) is a scalar variable (often representing an eigenvalue).Iis the identity matrix of the same dimension as A.det(...)denotes the determinant of the matrix.
For a 3x3 matrix A = [[a11, a12, a13], [a21, a22, a23], [a31, a32, a33]], the characteristic polynomial will be of the form c3λ³ + c2λ² + c1λ + c0.