Sentence examples for matrices are always from inspiring English sources

Usually, if not explicitly specified, matrices are always assumed to have compatible dimensions.

Furthermore, the scaling matrices are always chosen as the constant matrices in the previous combination synchronization schemes within two drive systems and one response system.

Even though the correlation matrices are always symmetric, hence in practice requiring the computation only of half of their entries, the computational overhead for such a procedure is of complexity O ( N 2 ).

The first model has 0 df, and hence the implied and observed covariance matrices are always equal, and the χ2 is equal to zero.

We can roughly call these series permutative the number of ones is similar (e.g., for unitary matrices is always equal to 4), but they occupy other positions in series.

The maximum observed differences between two independent (50,000 iterations each) estimates of the covariance matrices were always less than approximately 10% of the smallest estimated covariance, indicating good convergence between runs.

The eigenvalues λ1,..., λ M of a M × M covariance matrix are always indexed such that λ1≥ λ2... ≥ λ M, and the corresponding KLT matrix has the structure T = ( u 1 T, …, u M T ), where u m is the eigenvector associated λ m.

Therefore, if the squared norm of hierarchical signal differences with indices not being in the same row of XC matrix are always larger or equal than the bound, ∥ u c A c B - u c A ′ c B ′ ∥ 2 ≥ | α | 2 δ min 2, (21).

The diagonal elements of the similarity matrix are always 1, indicating that each centroid is most similar to itself.

This implies that the A-matrix is always diagonal.

A blank matrix is always desired for all types of quantitative analyses.