Sentence examples for matrix and det from inspiring English sources
where M = a b c d is the parameter matrix and det(M) = ad - bc = 1.
Superscript T stands for transpose, I 3 denotes a 3 × 3 identity matrix, and det means computing the determinant of matrix.
I n ∈ R n × n denotes the identity matrix and Det ( M ) the determinant of the matrix M. Let S ( t ), E ( t ), I ( t ) and R ( t ) be, respectively, the susceptible, infected (or exposed), infectious and removed-by-immunity populations at time t.
Because the matrix T = ( − λ i λ j cos φ i j ) i, j = 1 n + 1 is also a positive definite symmetric matrix and det G = 0, the matrix G is a semi-positive definite symmetric matrix and the rank of matrix G is n + 1.
where (boldsymbol {I}_{N_{R}}) is the N R ×N R identity matrix, (boldsymbol {beta } = text {diag}{left [beta _{1},beta _{2},cdots,beta _{N_{R}}right ]} in mathbb {C}^{N_{R} times N_{R}} ) is diagonal matrix, and det denotes the matrix determinant.
A matrix A is called an M-matrix if there exist a nonnegative matrix B and a real number s > ρ ( B ) such that A = s I − B, where ρ ( B ) is the spectral radius of B. It is well known that A is an H-matrix if and only if μ ( A ) is an M-matrix, and if A is an M-matrix, then the Schur complement of A is also an M-matrix and det A > 0 (see [3]).
Shortly, tr ( M k ) ≡ tr ( M l ) ≡ tr ( M ) mod d, where tr denotes the trace of these matrices, and det M k ≡ det M l ≡ det M mod d.
where A, B ∈ R n × n are given matrices and det ( A + B ) ≠ 0 ; f, g : [ 0, T ] × R n → R n and I i : R n → R n are given functions; Δ x ( t i ) = x ( t i + ) − x ( t i − ), where x ( t i + ) = lim h → 0 + x ( t i + h ), x ( t i − ) = lim h → 0 + x ( t i − h ) = x ( t i ). are the right- and left-hand limits of x ( t ) at t = t i, respectively.
Moreover, we have M = - ( V - 1 V ( S ) = - Adj + H φ det + H φ ( S ′ + H S , where Adj A) denotes the adjoint matrix of A and det(A) denotes the determinant of A. In the remaining of this section, we shall prove some uniqueness theorems for vectorial Sturm-Liouville equations.
Both R 1 ( 1 ) and Rt are continuous functions of the entries of the covariance matrix, and the log-det operator is concave on the set of Hermitian positive semi-definite matrices with bounded trace.
Thus the two matrices are positive definite and (det left (boldsymbol {F}^{(1)}left (frac {PT}{M}epsilon _{text {th}}^{2} right) right)) and (det left (boldsymbol {F}^{(r)}left (4epsilon _{text {th}}^{2} right)right)) are log-concave functions since the determinant of a positive definite matrix is log-concave [31].
