Sentence examples for matrices and let from inspiring English sources

Moreover, let A1, …, As be a family of d×d matrices over a noncommutative probability space (A, ϕ), let D⊂Md(A) denote the algebra of scalar diagonal matrices, and let C be the subalgebra of Md(A) generated by {A1, …, As}∪D.

In the following, let denote the set of real matrices and let denote the subset of consisting of symmetric matrices.

Let (C^{mtimes n}) ((R^{mtimes n})) be the set of all complex (real) matrices and let (mathbb{M}_{n}^) be the positive definite Hermitian matrices.

Let (mathcal{B}=(b_{n,k}(i))) be a sequence of infinite matrices, and let ((a_{n})) and ((b_{n})) be sequences of non-negative integers.

Let A 1, A 2 ∈ M n ( C ) be accretive-dissipative matrices and let A 1 = B 1 + i C 1, A 2 = B 2 + i C 2. be the Hermitian decompositions of these matrices.

In this section, we let (M_{n}) be the Hilbert space of (ntimes n) complex matrices and let (Vert cdot Vert ) stand for any unitarily invariant norm on (M_{n}), i.e. (Vert UTVVert =Vert TVert ) for all (Tin M_{n}) and for all unitary matrices (U,Vin M_{n}).

Let ξ be any design on a compact space X⊂Rm with a nonsingular information matrix, and let m+ε be the maximum of the variance function d ξ,x) over all x∈X.

Theorem 2.2 Let A, B = ( b i j ) ∈ R n × n be two nonsingular M-matrices, and let A − 1 = ( β i j ).

Then all the eigenvalues of A lie in the region ⋃ i, j = 1 i ≠ j n { z ∈ C : | z − a i i | | z − a j j | ≤ ( x i ∑ k ≠ i 1 x k | a k i | ) ( x j ∑ k ≠ j 1 x k | a k j | ) }. Theorem 2.1 Let A, B = ( b i j ) ∈ R n × n be two nonsingular M-matrices, and let A − 1 = ( β i j ).

M-matrix, and let A - 1 = ( a i j ′ ).

Let C be a fixed positive definite matrix and let matrix H solve matrix equation (6).