Sentence examples for matrices were first from inspiring English sources

Interpolated Young and Heinz inequalities for numbers and matrices were first given in [3].

Hausdorff matrices were first introduced by Hurwitz and Silverman (1917) as the collection of lower triangular matrices that commute with the Cesàro matrix of order one.

These distance matrices were first analyzed to produce "ordinations".

To address this, data matrices were first aligned by APGIII order.

Using Pearson's correlation coefficient (r) as a metric of similarity between expression values, correlation matrices were first calculated.

Distances within matrices were first ranked because the principal question concerned whether the relative magnitudes of variation were correlated.

To this end, the distribution of the singular values of random uniform matrices is first studied.

Specifically, the non-symmetric coefficient matrices are first decomposed into symmetric and skew-symmetric parts and the physical significance of each part is discussed.

System matrices are first obtained by using a general system identification technique, and then the natural frequency and damping ratio of each mode are extracted from the obtained system matrices.

Each of the two matrices was first converted into a vector.

For DNA sequences, PAM matrices are first computed.