# Vector Transformations and Eigenvectors of 2×2 Matrix

Vector Transformations and Eigenvectors of 2×2 Matrix

This Demonstration shows the transformation represented by a matrix applied to a vector . The vector is transformed to a new vector , shown in color. If the vector is an eigenvector of , then is simply scaled by , the eigenvalue, without changing direction (except the direction is reversed if .) Color-coded formulas show the calculation of the inverse, determinant and new vector , as well as the eigenvectors of .

22

A

21

x

x

b

x

A

b

λ

λ<0

b

A

If matrix is singular and has no inverse, it is indicated.

A