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