Square matrix

About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.

Method of generating matrix factors for a finite-dimensional linear transform

Abstract: A method of generating matrix factors for a finite-dimensional linear transform using a computer. The linear transform is represented by data values stored in a linear transformation matrix having a nonzero determinant. In one aspect, a first LU-decomposition is applied to the linear transformation matrix. Four matrices are generated from the LU-decomposition, including a first permutation matrix, a second permutation matrix, a lower triangular matrix having a unit diagonal, and a first upper triangular matrix. Additional elements include a third matrix Â, a signed permutation matrix Π such that A=ΠÂ, a permuted linear transformation matrix A′, a second upper triangular matrix U1, wherein the second upper triangular matrix satisfies the relationship Â=U1A′. The permuted linear transformation matrix is factored into a product including a lower triangular matrix L and an upper triangular matrix U. The linear transformation matrix is expressed as a product of the matrix factors.

Elastic deformation detecting method and ultrasonograph

Abstract: PROBLEM TO BE SOLVED: To obtain an elastic deformation detecting method within a flexible organization by normalizing elastic coefficient estimated amount by using a diagonal normalizing matrix having shaft direction change functions to be imparted to each basic elastic coefficient value as coefficients so as to store each value within a uniform interval fixing a center in the vicinity of a specific average value. SOLUTION: The definition of a normalizing matrix R is to uniformly keep vector formed by a distance from an average value of an element e1 of an elastic coefficient vector (e). Uniform interval is defined and the normalizing matrix R is obtained from a sensitivity matrix S by using a simple matrix calculation to be executed in a system 200. At the last of a calculation 222 calculating the matrix R, an electronic system 200 related to an ultrasonograph executes a calculation 223 calculating a matrix M of estimated amount of the vector (e) and continuously executes a calculation 224 of a matrix multiplication of the matrix M and vector (d). By a repetition, a method to be enforced in the electronic system 200 related to the ultrasonograph is utilized and a reproduced image of the elastic coefficient (e) can be acquired based on change vector.

Generating matrices to be used for the random orthogonal transformation of blocks of data in a transmission chain

Abstract: Matrices to be used for the random orthogonal transformation of blocks of data in a transmission chain are generated. A square matrix with orthogonal column vectors and orthogonal row vectors is divided to create M matrices. The number of rows of each of these matrices is equal to M*n, where n is the number of columns of each of the matrices and M is an integer larger than one. Each of the M matrices is allocated to a transmitter in a transmission chain or, alternatively, a plurality of the M matrices are allocated to one base station of a wireless transmission system.