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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.
