Sentence examples for matrix products in from inspiring English sources

In this case, the matrix products in (2) reduce to the products and powers of real numbers.

First, there are the matrix products in Proposition 3. is a row vector and its dimensions depend directly on the resolution of the data used.

The present author first introduced matrix rank formulas into the analysis of reverse-order laws of generalized inverses of matrix products in [25].

Establish analytical formulas for calculating the maximum and minimum ranks of the multiple matrix products in (3.65 - 3.108), and characterize the performances of these products via the rank formulas.

Equations (3.2 - 3.64) show that the matrix products in (3.1) are in fact a group of linear or nonlinear matrix-valued functions with one or more independent variable matrices.

(b) Establish analytical formulas for calculating the maximum and minimum ranks of the multiple matrix products in (3.65 - 3.108), and characterize the performances of these products via the rank formulas.  .

The STP of matrices, on the other hand, extends the conventional matrix product in cases of unequal dimensions.

Note that the matrix product in (11) requires only O M · d R multiplications, i.e., it is linear in M.

This can be achieved by testing each matrix product in the cartesian basis or directly when generating the point group elements.

The proposed algorithm is based on the semi-tensor product (STP) [21, 22], a novel matrix product that works by extending the conventional matrix product in cases of unequal dimensions.

We use | ⋅ | and to denote the norm and the inner product in R 2 and use z = ( u, v ) to denote an element in R 2 and E. Bz denotes the matrix product in R 2 for a 2 × 2 matrix B and z = ( u, v ) ∈ R 2. We use 0 to denote the origin in various spaces.