(When the number of dimensions of the domain and image differ, this volume is zero, so that such "determinants" are never considered.) For instance, a rotation preserves the volumes, so that the determinant of a rotation matrix is always 1. The inverse of a linear transform corresponds to the matrix inverse.Ī determinant measures the volume of the image of a unit cube by the transformation it is a single number. The composition of two linear transforms corresponds to the product of their matrices. The size of the matrix tells you the number of dimension of the domain and the image spaces. So a linear transform can be represented by an array of coefficients. They map points/lines/planes to point/lines /planes. ![]() (Linearity means that the image of a sum is the sum of the images.) Examples of linear transforms are rotations, scalings, projections. ![]() A matrix is a compact but general way to represent any linear transform.
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