1. In other words, the bilinear form determines a linear mapping 2. Let be a linear mapping between Banach spaces. 3. There it denotes general linear mappings between operators. 4. It follows from the Banach Steinhaus theorem that the linear mappings are uniformly bounded by some constant. 5. Therefore the matrix can be written down but does not represent a linear mapping in the straightforward sense. 6. Logarithmic spirals, including circles, can for instance be detected by ( complex ) convolutions and non-linear mappings . 7. "' Linear algebra "'is the branch of mathematics concerning vector spaces and linear mappings between such spaces. 8. The linear mapping operation is not unitary and thus will require a number of repetitions as it has some probability of failing. 9. When the determinant is equal to one, the linear mapping defined by the matrix is equi-areal and orientation-preserving. 10. Like kernel PCA they use a kernel function to form a non linear mapping ( in the form of a Gaussian process ).
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