Sentence examples for groups of matrices from inspiring English sources

Here we concentrate on, permutation groups, symmetry groups, and groups of matrices.

The theory of Lie algebras and Lie groups shows that there are only a few sensible ways to measure properties of figures in a linear space and that these methods yield groups of motions leaving the figures, which are (more or less) groups of matrices, unaltered.

Daniel Quillen's definition of the higher algebraic K-groups of a ring emphasized the importance of computing the homology of groups of matrices.

We have the following lemma regarding the relationships between the two groups of matrices as N→∞.

The theme is the development of the computing of the homology of the groups of matrices from Daniel Quillen's definitions of the higher algebraic K-groups.

It is well known that linear groups (that is subgroups of groups of matrices (GL_N Bbbk )), where (Bbbk ) is a field) is quite a restrictive class of groups as the Tits alternative [48] holds for them.

Various groups of matrix metalloproteases/ADAMs have been shown to be involved in the formation of new vessels during tumor growth [ 137].

Nonetheless, if one restricts G to be a linear group (group of matrices), the answer is positive (Schur, 1911).

The same holds true for G-weakly invariant designs, G being any compact group of matrices.

In this Note, we state a polynomial characterization of weakly invariant designs and show how to derive the construction of weakly invariant designs for the action of a compact group of matrices on an experimental domain, whose interior is not empty, from the construction of rotatable designs.

The following subgroup of this group (of matrices over the field (mathbb {F}_2)) was considered in [38].