A matrix is a rectangular array of elements - usually numbers. These, together with rules governing their addition and multiplication make up matrix algebra or system.
True
When the matrix of coefficients is singular.
Consider the linear system of equations AX = YwhereX is a n x 1 matrix of variables,Y is a n x 1 matrix of constants, andA is an n x n matrix of coefficients.Provided A is not a singular matrix, A has an inverse, A-1, an n x n matrix.Premultiplying by A-1 gives A-1AX = A-1Y or X = A-1Y, the solution to the linear system.
A = coefficient matrix (n x n) B = constant matrix (n x 1)
An idempotent matrix is a matrix which gives the same matrix if we multiply with the same. in simple words,square of the matrix is equal to the same matrix. if M is our matrix,then MM=M. then M is a idempotent matrix.
A Hadamard Matrix is a square matrix composed of 1 or -1. Using a square matrix system the hadamard matrix could be created
It is an element of the matrix. This could be a numerical value or an algebraic expression.
Is a matrix that shows the protection level accross several domains.
constant matrix
Rank of a matrix is used to find consistency of linear system of equations.As we know most of the engineering problems land up with the problem of finding solution of a linear system of equations ,at that point rank of matrix is useful.
The Hamiltonian matrix in quantum mechanics is important because it represents the total energy of a system. It contains information about the potential and kinetic energies of particles in the system. By solving the eigenvalue equation of the Hamiltonian matrix, we can determine the energy levels of the system, which correspond to the possible states that the system can occupy.
The service system design matrix define the relationship between sales opportunity and production efficiency measured against the amount of human interactive .
True
When its matrix is non-singular.
When the matrix of coefficients is singular.
To find the matrix representation of the operator Sz in the Sx basis for a spin 1/2 system, you can use the Pauli matrices. The matrix representation of Sz in the Sx basis is given by the matrix 0 0; 0 1.
A sparse matrix is matrix that allows special techniques to take advantage of large number of zero element. Application of sparse matrix is classification and relationship analysis in large data base system - SPARCOM