31. For linear transformations f : V \ to W, uniform continuity is equivalent to continuity. 32. This operator is a continuous linear transformation on D ( " U " ). 33. It is also the group of determinant-preserving linear transformations of the exceptional Jordan algebra. 34. Note that active transformations make sense even as a linear transformation into a different vector space. 35. Matrices allow arbitrary linear transformations to be represented in a consistent format, suitable for computation. 36. The above described transformation is a linear transformation from the CIE RGB space to XYZ space. 37. This group biholomorphically acts on the complex upper half-plane by fractional-linear transformations , 38. Thus the overall Mahler volume of " B " is preserved by linear transformations . 39. However, in summary, a linear transformation can just be thought of as a matrix. 40. A general linear transformation of this type has 2 2 " n " dimensions.
