Chapter 4. Numerical Interpretation of Eigenvalues In terms of matrix arithmetic eigenvalues turn matrix multiplication into scalar multiplication. Numerically.

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Presentation transcript:

Chapter 4

Numerical Interpretation of Eigenvalues In terms of matrix arithmetic eigenvalues turn matrix multiplication into scalar multiplication. Numerically knowing an eigenvalue tremendously lowers the number of operations required to get the result of a matrix multiplication. This optimizes the performance of certain algorithms that are used in the areas of computer graphics and engineering. The question that arises in this chapter is how can we determine what the eigenvalues and eigenvectors of a matrix are? What properties do eigenvalues of a matrix have?

x y Vectors on the positive x -axis are sent to negative x -axis and visa versa. While vectors on the y -axis remain fixed.