In other words, it does not matter whether you apply the linear map before or after the operations of addition and scalar multiplication. This is equivalent to requiring the same for any linear pdf of linear transformation of vectors, i. It is then necessary to specify which of these ground fields is being used in the definition of “linear”.
This is useful because it allows concrete calculations. A single linear map may be represented by many matrices. This is because the values of the elements of a matrix depend on the bases chosen. This case is discussed in more detail below.
Its image consists of all sequences with first element 0, and thus its cokernel consists of the classes of sequences with identical first element. Its image is the entire target space, and hence its co-kernel has dimension 0, but since it maps all sequences in which only the first element is non-zero to the zero sequence, its kernel has dimension 1. This gives an indication of how many solutions or how many constraints one has: if mapping from a larger space to a smaller one, the map may be onto, and thus will have degrees of freedom even without constraints. Conversely, if mapping from a smaller space to a larger one, the map cannot be onto, and thus one will have constraints even without degrees of freedom. No classification of linear maps could hope to be exhaustive. The following incomplete list enumerates some important classifications that do not require any additional structure on the vector space. 3 Vector spaces associated with a matrix or linear transformation, p.
This page was last edited on 14 November 2017, at 01:06. RGB color space and location of the primaries. Note that the colors in this displayed file are being specified using sRGB. Areas outside the triangle cannot be accurately colored because they are out of the gamut of sRGB therefore they have been interpreted.
This specification allowed sRGB to be directly displayed on typical CRT monitors of the time, which greatly aided its acceptance. R, G, and B it is not possible to represent colors outside this triangle, which is well inside the range of colors visible to a human with normal trichromatic vision. Below a compressed value of 0. 04045 or a linear intensity of 0. 00313, the curve is linear so the gamma is 1.