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The eigen values of a matirx are the values L such that Ax = Lx
where A is a matrix, x is a vector, and L is a constant.
The vector x is known as the eigenvector.
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What is the null matrix?
the matrix whose entries are all 0
What does it mean for a matrix to be triangular?
A square matrix in which all the entries of the main diagonal are zero
What is a minor diagonal matrix?
A minor diagonal matrix is one where the only non-zero entries are along the diagonal that runs from bottom most left to upper most right.
What is the formula of bordered Hessian matrix?
The bordered hessian matrix is used for fulfilling the second-order conditions for a maximum/minimum of a function of real variables subject to a constraint. The first row and first column of the bordered hessian correspond to the derivatives of the constraint whereas the other entries correspond to the second and cross partial derivatives of the real-valued function. Other than the bordered entries, the main diagonal of the sub matrix consists of entries for the second partial derivatives. All other entries of the sub matrix off of the main diagonal correspond to all combinations of cross partials. Evaluating the determinant of the bordered hessian will allow one to determine if the function attains its maximum or minimum at the stationary points, which by the way are limited in the fact that they must both satisfy the gradient equations and the constraint.
What is scalar multiplication?
Basically, you just multiply each entry in the matrix by a given number 4 1 3 5 -1-810-7-513 = 4 12 20 -4-3240-28-2052 In this case, there are 9 entries so your result is 9 corresponding entries which have been multiplied by 4.
What is a zero matrix?
A zero matrix is a matrix in which all of the entries are zero.
What is the null matrix?
the matrix whose entries are all 0
What is null matrix?
the matrix whose entries are all 0
What is the trace of a matrix to a power?
It is the diagonal entries of the matrix raised to a power.
What is the definition of a null matrix?
The null matrix is also called the zero matrix. It is a matrix with 0 in all its entries.
What does it mean for a matrix to be triangular?
A square matrix in which all the entries of the main diagonal are zero
What is the definition of unitary matrix?
It is the conjugate transpose of the matrix. Of course the conjugate parts only matters with complex entries. So here is a definition:A unitary matrix is a square matrix U whose entries are complex numbers and whose inverse is equal to its conjugate transpose U*. This means thatU*U = UU* = I. Where I is the identity matrix.
What are the following terms- eignvalues of matrix-entries of matrix-equality of matrix-matrix of groups-identity of matrix-inverse matrix-multiplication of matrices?
First, a small note: an m-by-n or m x n matrix has m rows and n columns.The eigenvalues λ of a matrix A are scalars such that Ax = λx for some nonzero x vector.The entries aij of a matrix A are the numbers contained within the matrix, each with a unique position of the ith row and jth column.'Equality' in matrices has the same definition as for the rest of mathematics.A matrix of groups is a matrix whose entries are members of a group, often with specific entries in certain positions.The matrix identity In is that square n by n matrix whose entries aij are 1 if i = j, and 0 if i ≠j.The inverse of a square matrix A is the square matrix B such that AB = In, denoted by B = A-1.Matrix multiplication is the act of combining two matrices, the p-by-q A = (aij) and the q-by-r B = (bij) to form the new matrix p-by-r C = (cij) such that cij = Σaikbkj, where 1 ≤ k ≤ q. This is denoted by C = AB. Note that matrix mulplication is not commutative, i.e. AB does not necessarily equal BA; the order of the components is important and must be maintained to achieve the result. Note also that although p does not need to equal r, q must be the same in each matrix.
What are disadvantages of sparse matrix in data structure using c?
what is the disadvantage of sparse matrix?
What is Random Matrix Theory?
The Random Matrix Theory provides an understanding of the dynamic properties of matrices using randomly drawn entries from diverse probability distributions.
What is a minor diagonal matrix?
A minor diagonal matrix is one where the only non-zero entries are along the diagonal that runs from bottom most left to upper most right.
Can a 3 by 3 matrix equal zero?
First we need to ask what you mean by a matrix equalling a number? A matrix is a rectangular array of numbers all of which might be zero and this is called the zero matrix. We can take the determinant of a square matrix such as a 3x3 and this may be zero even without the entries being zero.
