Note on Inner Products in Vector Spaces.
Note on inverse iteration and III-conditioned eigensystems
Note on Matrices with a Very Ill-Conditioned Eigenproblem.
Note on some greatest common divisor matrices
Some quadratic forms related to "greatest common divisor matrices" are represented in terms of L²-norms of rather simple functions. Our formula is especially useful when the size of the matrix grows, and we will study the asymptotic behaviour of the smallest and largest eigenvalues. Indeed, a sharp bound in terms of the zeta function is obtained. Our leading example is a hybrid between Hilbert's matrix and Smith's matrix.
Note on strongly nil clean elements in rings
Let be an associative unital ring and let be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results.
Note on the ANOVA of a completely confounded factorial experiment
The purpose of this paper is to present a modern approach to the analysis of variance (ANOVA) of disconnected resolvable group divisible partially balanced incomplete block (GDPBIB) designs with factorial structure and with some interaction effects completely confounded. A characterization of a factorial experiment with completely confounded interaction is given. The treatment effect estimators and some relations between the matrix F of the reduced normal equations and the information matrix A are...
Note on the core matrix partial ordering
Complementing the work of Baksalary and Trenkler [2], we announce some results characterizing the core matrix partial ordering.
Note on the degree of concavity of the determinant on sets of positive definite quadratic forms.
Note on the numerical solutions of the general matrix convolution equations by using the iterative methods and box convolution product.
Note sur le rang d'une matrice
Note zu dem Aufsatze "über eine Eigenschaft von Functionaldeterminanten" Bd. 69, p. 355 dieses Journals.
Notes on linear combinations of two tripotent, idempotent and involutive matrices that commute.
Notes on power LCM matrices
Notes on the divisibility of GCD and LCM matrices.
Notice on the Chipman generalization of the matrix inverse
Notiz über ternäre Formen mit verschwindender Functionaldeterminante
Nové poučky o determinantech
Nový důkaz poučky o poměrech mezi původními a přidruženými determinanty a subdeterminanty
n-supercyclic and strongly n-supercyclic operators in finite dimensions
We prove that on , there is no n-supercyclic operator with 1 ≤ n < ⌊(N + 1)/2⌋, i.e. if has an n-dimensional subspace whose orbit under is dense in , then n is greater than ⌊(N + 1)/2⌋. Moreover, this value is optimal. We then consider the case of strongly n-supercyclic operators. An operator is strongly n-supercyclic if has an n-dimensional subspace whose orbit under T is dense in , the nth Grassmannian. We prove that strong n-supercyclicity does not occur non-trivially in finite...
Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric -stable processes.