| 41. | While studying compositions of linear transformations, Arthur Cayley was led to define matrix multiplication and inverses.
|
| 42. | Linear transformations are global in nature, thus, they cannot model local geometric differences between images.
|
| 43. | The reflection of a point " x " about this hyperplane is the linear transformation:
|
| 44. | Mahalanobis distance is preserved under full-rank linear transformations of the space spanned by the data.
|
| 45. | Accordingly, every invertible linear transformation of a finite-dimensional linear topological space is a homeomorphism.
|
| 46. | Galilean scale relativity involves linear transformations a constant fractal dimension, self-similarity and scale invariance.
|
| 47. | The theory of ordinary similarity arises as a result of studying linear transformations referred to different bases.
|
| 48. | It is not classified as a linear transformation, but is instead known as an affine transformation.
|
| 49. | All of the integral transforms can be expressed as linear transformations; that is, as matrices.
|
| 50. | However, often the definition of the G�teaux differential also requires that it be a continuous linear transformation.
|
