Sentence examples for matrix and let from inspiring English sources

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.

Let A ≥ 0 be an n × n matrix and let ρ ( A ) < 1.

Let the spectral decomposition of be, where is an orthogonal matrix and Let, then (3.15).

Let be an complex square matrix and let be the eigenvalues of, then (2.1).

Let Ω be a diagonal and positive-definite matrix, and let γ be a positive constant.

Let (A=(a_{n,k})) be a nonnegative weighted regular matrix and let (Esubseteqmathbb {N}).

The self-repair microcapsules in the epoxy resin would break as a result of microcrack expansion in the matrix, and letting out the strong repair agent to recover the mechanical strength with a relative healing efficiency of up to 140% which is a ratio of healed property value to initial property value or healing efficiency up to 119% if using the healed strength with the damaged strength.

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.

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

Theorem 2.3 Let A = ( a i j ) ∈ R n × n be an M-matrix, and let A − 1 = ( β i j ) be a doubly stochastic matrix.

Corollary 2.1 Let A = ( a i j ) ∈ R n × n be an M-matrix, and let A − 1 = ( β i j ) be a doubly stochastic matrix.