`\text{Characteristic Polynomial} = lambda^2 + (-(A11+A22))lambda+((A11*A22)+(-(A21*A12)))`

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The characteristic polynomial (CP) of a 2x2 matrix calculator computes the characteristic polynomial of a 2x2 matrix.

INSTRUCTIONS: Enter the following:

• (A)  This is the 2x2 matrix.

Polynomial: The calculator returns the polynomial.  

Matrix Calculators

• Compute the Trace of a 2x2 Matrix
• Compute the Determinant of a 2x2 Matrix
• Compute the Inverse of a 2x2 Matrix
• Compute the Eigenvalues of a 2x2 Matrix
• Classifying Equilibria of a 2x2 Matrix
• Compute the Eigenvalues and Eigenvectors of a 2x2 Matrix
• Multiply a 2x2 matrix by a scalar
• Characteristic Polynomial of a 3x3 Matrix

General Information

The characteristic polynomial of a 2x2 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 the trace and determinant of the matrix.

For a 2x2 matrix, the characteristic polynomial is `λ^2-("trace")λ+("determinant")`, so the eigenvalues `λ_(1,2)` are given by the quadratic formula:

`λ_(1,2)=(("trace")+-sqrt(("trace")^2-4("determinant")))/(2)`