Question

In: Advanced Math

Consider the linear transformation T: R2x2 -> R2x2 defined by T(A) = AT - A. Determine...

Consider the linear transformation T: R^2x2 -> R^2x2 defined by T(A) = A^T - A.

Determine the eigenvalues of this linear transformation and their algebraic and geometric multiplicities.

Expert Solution

Solution:

Let be the standard basis for .

The characteristic equation is

For

By

For

By

Algebraic Multiplicity of is

Geometric Multiplicity of is

Algebraic Multiplicity of is

Geometric Multiplicity of is

Colby Messinger answered 2 years ago

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