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Eigenvalues & Eigenvectors - University of Kentucky

Eigenvalues & Eigenvectors Example Suppose . Then . So, geometrically, multiplying a vector in by the matrix A results in a vector which is a reflection of the given vector about the y-axis. We observe that and . Thus, vectors on the coordinate axes get mapped to vectors on the same coordinate axis. That is, for vectors on the coordinate axes we see that and are parallel or, equivalently, for vectors on the coordinate axes there exists a scalar so that . In particular, for vectors on the x-axis and for vectors on the y-axis. Given the geometric properties of we see that has solutions only when is on one of the coordinate axes.

Eigenvalues & Eigenvectors Example Suppose . Then . So, geometrically, multiplying a vector in by the matrix A results in a vector which is a reflection of the given vector about the y-axis. We observe that and. Thus, vectors on the coordinate axes get mapped to vectors on the same coordinate axis. That is,

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