Sentence examples for matrix expression with from inspiring English sources

Given a matrix expression with some variant matrices in it, the rank of the matrix expression will vary with respect to the variant matrices.

Given a matrix with some variant entries in it (often called partial matrix) or a matrix expression with some variant matrices in it, the rank of the partial matrix or matrix expression will vary with respect to the variant entries or variant matrices.

Many problems in matrix theory and applications are closely related to the inequalities for ranks of matrix expressions with variant matrices.

Many problems in matrix theory and applications are closely related to maximal and minimal possible ranks of matrix expressions with variant entries.

We give in this article the maximal and minimal ranks of the matrix expression A-B1V1C1-B2V2C2-B3V3C3-B4V4C4 with respect to V1, V2, V3, and V4.

Thus, alterations in metabolism (eg, increased MMP expression and altered matrix expression) were associated with statin treatment.

With a matrix expression, the node voltage phasors v k, at iteration k, are obtained as follows: mathbf{v}_{k} = mathbf{Z}_{text{paths}}mathbf{x}_{k} (3).

With the matrix expression, we then formulate a CSFB matrix to construct a constrained reduced-tap (TRTap) receiver whose weight length can be far shorter than the length of the spreading code.

In the rest of this section, we will find the minimal rank of the linear matrix expression P V1,V2, V3, V4) in (4), with respect to four variant matrices V i ∈ C p i × q i, i = 1, 2, 3, 4, when P V1, V2, V3, V4) satisfy some restrictions.

In this article, given matrices A ∈ C m × n, B i ∈ C m × p i, C i ∈ C q i × n, i = 1, 2, 3, 4, we will present the maximal and minimal ranks of the matrix expression A-B1V1C1 - B2V2C2 - B3V3C3 - B4V4C4 with respect to V1, V2, V3, and V4.

This study built on previous findings that identified a reduction in matrix gene expression with joint ageing [ 7].