Sentence examples for matrix product a from inspiring English sources

Let A ∗ be the conjugated transpose of a complex matrix or a complex block matrix A, and let ∏ i = k 1 A i stand for a matrix product A k A k − 1 ⋯ A 1. Next we will present the solution of system (1).

The transmission channels are obtained by diagonalizing the matrix product A L = G a ∑ L G r, and can be interpreted as the scattering state through which the current can flow.

Although our study focused on the use of Integra® as a matrix product, any matrix formulation could be subjected to similar evaluation and explored for possible targeting peptides.

Each Point Forecast Matrix product has a 7-day forecast.

For a conventional matrix product, if Col (A) ≠ Row (B), then matrices A and B are multiplicative.

With direct calculation, it can be shown that where Mt is the transpose of M. From matrix product properties transpose(A × B) = transpose(B) × transpose(A), then plugging Eq. (12) into Eq. (6) results in On the other hand, plugging Eqs.

As an introductive example, consider computation of the matrix product AB, where A and B define matrices of sizes k m and m p, respectively.

According to the property of matrix product, pre-multiplying matrix E{A A H} by φ or post-multiplying it by φ H does not increases its rank, hence from (23), the rank of covariance matrix R satisfies begin{array}rcl@ {text{rank}left({{boldsymbol R} }right)} le {text{rank}left(E {{boldsymbol A} {boldsymbol A}^{mathrm{H}}} right)}, end{array} (25).

For the moment we will exclude the outer DFT matrices and determine the expectation value of the inner matrix product. is a circular Toeplitz matrix based on the channel impulse response, and was shown in Section 3.2 to be a matrix with zero entries except for the submatrix found in its upper right corner.

The mode- matrix product defines multiplication of a tensor with a matrix in mode.

The operator given in (2) stands for the Hadamard matrix product that is an element-by-element multiplication [20].