linear transformation in a sentence

Examples

1. While studying compositions of linear transformations, Arthur Cayley was led to define matrix multiplication and inverses.
2. Linear transformations are global in nature, thus, they cannot model local geometric differences between images.
3. The reflection of a point " x " about this hyperplane is the linear transformation:
4. Mahalanobis distance is preserved under full-rank linear transformations of the space spanned by the data.
5. Accordingly, every invertible linear transformation of a finite-dimensional linear topological space is a homeomorphism.
6. Galilean scale relativity involves linear transformations a constant fractal dimension, self-similarity and scale invariance.
7. The theory of ordinary similarity arises as a result of studying linear transformations referred to different bases.
8. It is not classified as a linear transformation, but is instead known as an affine transformation.
9. All of the integral transforms can be expressed as linear transformations; that is, as matrices.
10. However, often the definition of the G�teaux differential also requires that it be a continuous linear transformation.