Tsatsomeros: Principal minors, Part I: A method for computing all the principal minors of a matrix - Griffin, J () Citation Context ...matrices. The first matrix is [pm 2 n−1] which is the (n, n) entry of the
The class contains both the group and the Moore-Penrose generalized inverses of A. In an application of our results it is shown that the fundamental matrix of a continuous (in time) ergodic Markov chain on a finite state space has all its principal minors nonnegative.S.R. Mohan and M. ...
matrix minorsdeterminantal modelsThe algebraic relations between the principal minors of an $n\\times n$ matrixare somewhat mysterious, see e.g. [lin-sturmfels]. We show, however, that byadding in certain \\emph{almost} principal minors, the relations are generatedby a single relation, the ...
We prove that a polynomial map F = X + H k[X] with homogeneous H(k is a field of characteristic zero) is linear triangularizable if and only if the Jacobian matrix J(H) is a noncommutative-nilpotent matrix.doi:10.1080/03081087.2017.1354971Yan Tian...
In the literature one may encounter certain infinite tridiagonal matrices, the principal minors of which, constitute the Fibonacci or Lucas sequence. The major purpose of this article is to find new infinite matrices with this property. It is interesting to mention that the matrices found are not...
of the minors obtained by taking (distinct) rows \(i=(i_1, \dots , i_r)\) and columns \(1, \dots , r\) . in fact one can readily check that \(d=\det (a_{ij})_{1 \le i,j \le r}\) is a classical section and, denoting by \(\pi : {\mathcal {o}}(\mathrm {...
Charles R. JohnsonSivaram K. NarayanLinear Algebra and ApplicationsC.R. Johnson, S. Narayan, When the positivity of the leading principal minors implies the positivity of all principal minors of a matrix, Linear Algebra Appl., 439 (2013), 2934-2947....
One gives an elementary proof of the known fact that if the principal minors of an M -matrix with a positive determinant are nonnegative, then they are positive.doi:10.1007/BF01230264V. V. IshkhanovKluwer Academic Publishers-Plenum PublishersJournal of Soviet Mathematics...
t k = A t_k = t A^* if all the order- k k principal minors of B B are nonzero, and two of those minors are of opposite sign; t k = A + t_k = t A^+ (respectively, t k = A t_k = t A^- ) if all the order- k k principal minors of B B are positive (respect...
Thus the corresponding interpolation matrix M is nonsingular. Schumaker stated the conjecture that all principal submatrices of M are nonsingular too. Furthermore, all of the corresponding determinants (the principal minors) are conjectured to be positive. This result would solve the constrained ...