Let t ≥ 1 and let n, M be natural numbers, n < M. Let A = (a i,j) be an n × M matrix whose rows are orthonormal. Suppose that for all j M n · n i=1 a 2 i,j 1/2 ≤ t.

Let A be an n × n complex matrix and 0 ≤ q ≤ 1. The boundary of the q-numerical range of A is the orthogonal projection of a hypersurface defined by the dual surface of the homogeneous polynomial F (t, x, y, z) = det(t In + x(A + A )/2 + y(A−A)/(2i) + z AA). We construct different types of cubic surfaces SF corresponding to the homogeneous polynomial F (t, x, y, z) induced by some 3 × 3 matrice...

The computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. In this approach, a truncated Hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. Two illustrative...

In the dual-axis rotation inertial navigation system (INS), besides the gyro error, accelerometer error, rolling misalignment angle error, and the gimbal angle error, the shaft swing angle and the axis non-orthogonal angle also affect the attitude accuracy. Through the analysis of the structure, we can see that the shaft swing angle and axis non-orthogonal angle will produce coning errors which...

In this work is proposed a method using orthogonal matrix transform properties to encrypt and decrypt a message. It will be showed how to use matrix’s functions to create complex encryptions. Because orthogonal matrix are always diagonalizable on R, and the exponential of a diagonal matrix is easy to compute, the exponential of orthogonal matrix will be used to encrypt text messages.

In this paper we deal with orthogonal matrix polynomials. First of all, we establish some basic notations and results we need later. A matrix polynomial P is a matrix whose entries are polynomials, or, equivalently, a combination P(t) = A 0 +A 1 t+ +A n t n , where A 0 ; ; A n are numerical matrices (the size of all the matrices which appear in this paper is N N). A positive deenite matrix of m...

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

A logic network to produce the sequency ordered Hadamard matrix H based on the property of gray code and orthogonal group codes is developed. The network uses a counter to generate Rademacher function such that the output of H will be in sequency. A general purpose shift register with output logic is used to establish a sequence of period P corresponding to a given value of order m of the Hadam...

We consider aane systems in R n constructed from a given integral invertible and expansive matrix R, and a nite set B of translates, b x := R ?1 x + b; the corresponding measure on R n is a probability measure and xed by the selfsimilarity = jBj ?1 P b2B ?1 b. There are two a priori candidates for an associated orthogonal harmonic analysis : (i) the existence of some subset in R n such that the...

In this paper, the notions of $(T,S)$-composition matrix and$(T,S)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(T,S)$ is a dual pair of triangular module. Theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. Furthermore, theirproperties and characterizations are presented. Then a new methodbased on $tilde{...