1. Geometrically, the inner product of two vectors can be considered a measure of their similarity.

2. In the inner product space, the existence theory of best approximation element was obtained and described.

3. The product is the inner product of x and y.

4. For this reason the inner product is called also the scalar product.

5. A new inner product of matrix is defined in this paper , which can save matching time.

6. Vector space model calculation, the inner product, outer product, addition, multiplication.

7. The inner product in interpolation interpretation is a residual and therefore can be precomputed successively.

8. The interpolation approximation is important, because the computation of inner product is avoided.

9. Based on the minimizing vector theorem of the fuzzy inner product space, the pseudo fuzzy orthogonal vector is defined and the projected theorem of the fuzzy inner product space is testified.

10. The support vector machine has avoided the dimension disaster with the inner product operation.

11. In the DA-based implementation, the lookup table (LUT) stores all possible values of inner product of the fixed coefficients and the input bit vector.

12. A few good necessary and sufficient conditions are given by using inner product and length relation for antisymmetric transformation on Euclidean space.

12. try its best to gather and create good sentences.

13. The only involved operations are convolution, inversion , squar - root, subsumpling and inner product of sequenses.

14. The problem of finding stabilizer quantum-error-correcting codes can be transformed into the problem of finding additive self-orthogonal codes over the Galois field GF(4) under a trace inner product .