Eigenvalue & Eigenvector Calculator

Compute characteristic polynomial, eigenvalues, multiplicities, and eigenvectors for square matrices up to 6x6.

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What This Calculator Does

Compute characteristic polynomial, eigenvalues, multiplicities, and eigenvectors for square matrices up to 6x6.

It combines Matrix Size, a11, a12, a13 to estimate Characteristic Polynomial, Eigenvalues, Eigenvalue λ1.

Formula & Method

Core equations: characteristic polynomial is \det(\lambda I-A)=0; eigenvectors satisfy (A-\lambda I)v=0.

Notation used in the formulas: R = Characteristic Polynomial; x_{1} = Matrix Size; x_{2} = a11; x_{3} = a12; x_{4} = a13; x_{5} = a14; x_{6} = a15.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Inputs Used

Matrix Size: Used directly in the calculation.
a11: Used directly in the calculation.
a12: Used directly in the calculation.
a13: Used directly in the calculation.
a14: Used directly in the calculation.
a15: Used directly in the calculation.
a16: Used directly in the calculation.
a21: Used directly in the calculation.
a22: Used directly in the calculation.
a23: Used directly in the calculation.
a24: Used directly in the calculation.
a25: Used directly in the calculation.
a26: Used directly in the calculation.
a31: Used directly in the calculation.
a32: Used directly in the calculation.
a33: Used directly in the calculation.
a34: Used directly in the calculation.
a35: Used directly in the calculation.
a36: Used directly in the calculation.
a41: Used directly in the calculation.
a42: Used directly in the calculation.
a43: Used directly in the calculation.
a44: Used directly in the calculation.
a45: Used directly in the calculation.
a46: Used directly in the calculation.
a51: Used directly in the calculation.
a52: Used directly in the calculation.
a53: Used directly in the calculation.
a54: Used directly in the calculation.
a55: Used directly in the calculation.
a56: Used directly in the calculation.
a61: Used directly in the calculation.
a62: Used directly in the calculation.
a63: Used directly in the calculation.
a64: Used directly in the calculation.
a65: Used directly in the calculation.
a66: Used directly in the calculation.

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