The characteristic polynomial (CP) of a 3x3 matrix calculator computes the characteristic polynomial of a 3x3 matrix.
INSTRUCTIONS: Enter the following:
Polynomial: The calculator returns the polynomial.
The characteristic polynomial (CP) of an nxn matrix `A` is a polynomial whose roots are the eigenvalues of the matrix `A`. It is defined as `det(A-λI)`, where `I` is the identity matrix. The coefficients of the polynomial are determined by theand of the matrix.
For the 3x3 matrix A:
A = `[[A_11,A_12, A_13],[A_21,A_22,A_23],[A_31,A_32,A_33]]`,
the characteristic polynomial can be found using the formula `-λ^3+"tr"(A)λ^2+1/2("tr"(A)^2-"tr"(A^2))λ+det(A)`, where `"tr"(A)` is the trace of `A` and `det(A)` is the determinant of `A`.
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