Special cases of linear mappings (a) Rotations around the origin Let
... Such a polynomial has at most n zeros, so A can have at most n different eigenvalues. Attention: There are matrices which have no (real) eigenvalues at all! Example: Rotation matrices with angle ϕ ≠ 0°, 180°. ...
... Such a polynomial has at most n zeros, so A can have at most n different eigenvalues. Attention: There are matrices which have no (real) eigenvalues at all! Example: Rotation matrices with angle ϕ ≠ 0°, 180°. ...
3D Geometry for Computer Graphics
... Diagonalizable matrix is essentially a scaling. Most matrices are not diagonalizable – they do other things along with scaling (such as rotation) So, to understand how general matrices behave, only eigenvalues are not enough SVD tells us how general linear transformations behave, and other things… ...
... Diagonalizable matrix is essentially a scaling. Most matrices are not diagonalizable – they do other things along with scaling (such as rotation) So, to understand how general matrices behave, only eigenvalues are not enough SVD tells us how general linear transformations behave, and other things… ...
