Characteristic Polynomial of a 3x3 Matrix

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Equation / Last modified by KurtHeckman on 2017/05/15 19:17
`CP = `
Characteristic Polynomial of a 3x3 Matrix
Variable Instructions Datatype
`(A)" 3x3 Matrix"` Enter the 3x3 matrix. Matrix
Rating
ID
SavannahBergen.Characteristic Polynomial of a 3x3 Matrix
UUID
1fe0a0b6-1ea2-11e6-9770-bc764e2038f2

The characteristic polynomial (CP) of a 3x3 matrix calculator computes the characteristic polynomial of a 3x3 matrix.

INSTRUCTIONS: Enter the following:

  • (A)  This is the 3x3 matrix.

Polynomial: The calculator returns the polynomial.  

Related Calculators:

  • To compute the product of a 3x3 matrix and a 3x1 matrix, CLICK HERE.
  • To compute the Mirror of a 3x3 Matrix, CLICK HERE
  • To compute the Inverse of a 3x3 Matrix, CLICK HERE.
  • To compute the Transpose of a 3x3 Matrix, CLICK HERE.
  • To compute the Trace of a 3x3 Matrix, CLICK HERE.

The Math

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 the determinant and trace 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+("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`.

Characteristic Polynomial for a 2x2 Matrix

For theCharacteristic Polynomial of a 2x2 matrix, CLICK HERE

 

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