Sentence examples similar to matrix then exists from inspiring English sources

If is a nonsingular -matrix, then exists and (2.46).

Let be a square complex matrix, then there exists an invertible matrix such that (2.14).

If A is a n × n Hermitian matrix, then there exists a unitary matrix U such that A = U*[λ1,...,λ n ]U, where [λ1,...,λ n ] is diagonal matrix and λ i (i = 1,2,...,n) are eigenvalues of A, respectively.

If A is an M matrix, then there exists a positive diagonal matrix (D=operatorname{diag}(d_{1},ldots,d_{n},d_{i}>0, (d_{i=10),ldots,ndotsuch, such that matrix (B= frac{1}{2}(DA+A^{T}D)) is positive definite.

Suppose that (mathscr{A}) is an n order matrix, then there exist (mathscr{B}inmathbb{R}^{ntimes n}) and an integer (rgeq1) satisfying B A B T = ( A 1 A 12 ⋯ A 1 r 0 A 2 ⋯ A 2 r ⋮ ⋮ ⋱ ⋮ 0 0 ⋯ A r ), where (mathscr{A}_{1}), (mathscr{A}_{2}), … , (mathscr{A}) are square irreducible matrices.

Then exists.

If, then exists.

If converges, then exists.

If and, then exists.

Then, exists for all.

Then exists such that (4.4).