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A strictly diagonally dominant matrix (or an irreducibly diagonally dominant matrix [2]) is non-singular. A Hermitian diagonally dominant matrix with real non-negative diagonal entries is positive semidefinite. This follows from the eigenvalues being real, and Gershgorin's circle theorem. If the symmetry requirement is eliminated, such a matrix ...
A complex square matrix is said to be weakly chained diagonally dominant (WCDD) if A {\displaystyle A} is WDD and for each row i 1 {\displaystyle i_{1}} that is not SDD, there exists a walk i 1 → i 2 → ⋯ → i k {\displaystyle i_{1}\rightarrow i_{2}\rightarrow \cdots \rightarrow i_{k}} in the directed graph of A {\displaystyle A} ending ...
The binary matrix with ones on the anti-diagonal, and zeroes everywhere else. a ij = δ n+1−i,j: A permutation matrix. Hilbert matrix: a ij = (i + j − 1) −1. A Hankel matrix. Identity matrix: A square diagonal matrix, with all entries on the main diagonal equal to 1, and the rest 0. a ij = δ ij: Lehmer matrix: a ij = min(i, j) ÷ max(i, j).
The results indicated that alpha male Capuchin are the preferred mate for adult females. However, only the alpha females had strong interactions with the alpha males by virtue of a dominance hierarchy among the females in which only the most dominant and strong females were able to interact with the alpha male. [4]
Visual communication is a common dominance signal among animals. They are an effective modality as they come at a low cost to the animal and minimize risk. The Gila Monster (Heloderma suspectum) for example, express bright orange splotches during territorial conflict to warn competitors that they are poisonous, and thus assert their dominance over a territory.
For many animal societies, an individual's position in the dominance hierarchy corresponds with their opportunities to reproduce. [6] In hierarchically social animals, dominant individuals may exert control over others. For example, in a herd of feral goats it is a large male that is dominant and maintains discipline and coherence of the flock.
The adjugate of a diagonal matrix is again diagonal. Where all matrices are square, A matrix is diagonal if and only if it is triangular and normal. A matrix is diagonal if and only if it is both upper-and lower-triangular. A diagonal matrix is symmetric. The identity matrix I n and zero matrix are diagonal. A 1×1 matrix is always diagonal.
In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges.