منابع مشابه
determinant of the hankel matrix with binomial entries
abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.
15 صفحه اولOn the Determinant of Symplectic Matrices∗
A collection of new and old proofs showing that the determinant of any symplectic matrix is +1 is presented. Structured factorizations of symplectic matrices play a key role in several arguments. A constructive derivation of the symplectic analogue of the Cartan-Dieudonné theorem is one of the new proofs in this essay.
متن کاملRandom Matrices: Law of the Determinant
Let An be an n by n random matrix whose entries are independent real random variables with mean zero and variance one. We show that the logarithm of | detAn| satisfies a central limit theorem. More precisely, sup x∈R ̨̨̨ P ` log(| detAn|)− 12 log(n− 1)! q 1 2 logn ≤ x ́ − Φ(x) ̨̨̨ ≤ log 1 3+o(1) n.
متن کاملQuaternionic Matrices: Inversion and Determinant ∗
We discuss the Schur complement formula for quaternionic matrices, M , and give an efficient method to calculate the matrix inverse. We also introduce the functional D[M ] which extends to quaternionic matrices the non-negative number |det[M ]|. 1. Introduction. Much of the spectral theory of complex matrices does not extend to quaternion matrices without further modifications [1, 2, 3]. In par...
متن کاملDeterminant of Some Matrices of Field Elements
Here, we present determinants of some square matrices of field elements. First, the determinat of 2 ∗ 2 matrix is shown. Secondly, the determinants of zero matrix and unit matrix are shown, which are equal to 0 in the field and 1 in the field respectively. Thirdly, the determinant of diagonal matrix is shown, which is a product of all diagonal elements of the matrix. At the end, we prove that t...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1997
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(96)00147-4