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Student[LinearAlgebra][CharacteristicMatrix] - construct a characteristic Matrix

Calling Sequence

CharacteristicMatrix(A, t, options)

Parameters

A

-

square Matrix

t

-

name; variable

options

-

(optional) parameters; for a complete list, see LinearAlgebra[CharacteristicMatrix]

Description

• 

The CharacteristicMatrix(A, t) command constructs the characteristic Matrix M=Idt+A, where Id is the appropriately sized identity Matrix. The determinant of M, found by using DeterminantM, is the characteristic polynomial  of A.

Examples

withStudent[LinearAlgebra]:

A:=1,2,3|1,2,3|1,5,6

A:=111225336

(1)

C:=CharacteristicMatrixA,t

C:=t1112t2533t6

(2)

DeterminantC

t39t2

(3)

CharacteristicPolynomialA,t

t39t2

(4)

See Also

LinearAlgebra[CharacteristicMatrix], Student[LinearAlgebra], Student[LinearAlgebra][CharacteristicPolynomial], Student[LinearAlgebra][CompanionMatrix], Student[LinearAlgebra][Determinant], Student[LinearAlgebra][Eigenvalues]


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