Examples of using Square matrix in English and their translations into Russian
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Thus, we get a square matrix of judgments.
A square matrix that is not diagonalizable is called defective.
You can select the square matrix of averaging 3х3, 5х5, etc.
A square matrix has an inverse if and only if its determinant is not zero.
However, the upper-triangularization of an arbitrary square matrix does generalize to compact operators.
Although every square matrix has a Schur decomposition, in general this decomposition is not unique.
There are several techniques for lifting a real function to a square matrix function such that interesting properties are maintained.
As soon as to find characteristic polynomial, one need to calculate the determinant,characteristic polynomial can only be found for square matrix.
Input data: dense square matrix[math]A[/math] with entries[math]a_{ij}/math.
There obtained analogies of classical Cramer's formulas for systems of linear equations and inequalities with square matrix of coefficients from Boolean algebra.
The parallel version of the algorithm for multiplying a square matrix of order n by a vector requires that the following layers be successively performed.
A square matrix A is called invertible or non-singular if there exists a matrix B such that A B B A I n{\displaystyle AB=BA=I_{n.
Bridging the physical and digital,the street-level cut-outs also had QR codes, a square matrix barcode, that smartphone owners could scan to take them to the campaign application.
In linear algebra, a square matrix A{\displaystyle A} is called diagonalizable or nondefective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P{\displaystyle P} such that P- 1 A P{\displaystyle P^{-1}AP} is a diagonal matrix. .
The adjoint M* of a complex matrix M is the transpose of the conjugate of M:M* M T. A square matrix A is called normal if it commutes with its adjoint: A*A AA.
These matrices are used to rise a square matrix to a power, to extract the roots of the n-th degree of a square matrix, to calculate matrix exponent, etc.
The first restriction can be written as diag( A x+ b)≥ 0{\displaystyle{\textbf{diag}}(Ax+b)\geq 0} where the matrix diag( A x+ b){\displaystyle{\textbf{diag}}(Ax+b)}is the square matrix with values in the diagonal equal to the elements of the vector A x+ b{\displaystyle Ax+b.
Given an n× n square matrix A of real or complex numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation( A- λ I) k v 0,{\displaystyle\left(A-\lambda I\ right)^{ k}{\ mathbf{v}}=0,} where v is a nonzero n× 1 column vector, I is the n× n identity matrix, k is a positive integer, and both λ and v are allowed to be complex even when A is real.
Perron numbers are named after Oskar Perron; the Perron-Frobenius theorem asserts that, for a real square matrix with positive algebraic coefficients whose largest eigenvalue is greater than one, this eigenvalue is a Perron number.
This involves simulating the behaviour of the magnetospheric tail using a 60x100 square matrix, ensuring that a small border of the matrix is closed(this corresponds to the sector of the Earth's current sheet) while the other borders are open.
We introduce the programs-procedures for square matrices construction based on the selected models of canonical matrices. .
The matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
Similarity is an equivalence relation on the space of square matrices.
Any two square matrices of the same order can be added and multiplied.
Then you can create a certain amount of various square matrices based on canonical matrix models, it allows to use individual learning technologies.
We also construct the square matrices over arbitrary Boolean algebra which determine some Boolean binary relation and generate a cyclic semigroup with the maximum index and period.
The parallel version of the algorithm for multiplying square matrices of order n requires that the following layers be successively performed.
For arbitrary square matrices M{\displaystyle M}, N{\displaystyle N} we write M≥ N{\displaystyle M\geq N} if M- N≥ 0{\displaystyle M-N\geq 0} i.e., M- N{\displaystyle M-N} is positive semi-definite.
For example, the computational power of the dot product operation is[math]1[/math];the computational power of multiplying two square matrices is[math]2n/3/math.
In terms of the parallel form width, its complexity is also quadratic(for square matrices) or bilinear for general rectangular matrices. .