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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.
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What is the formula for the determinant of a 3 x 3 matrix?
If the matrix is { a1 b1 c1} {a2 b2 c2} {a3 b3 c3} then the determinant is a1b2c3 + b1c2a3 + c1a2b3 - (c1b2a3 + a1c2b3 + b1a2c3)
What is idempotent matrix?
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.
What is a reduced matrix?
Reduced matrix is a matrix where the elements of the matrix is reduced by eliminating the elements in the row which its aim is to make an identity matrix.
How are the inverse matrix and identity matrix related?
If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.
Each number in a matrix is called a?
Each number in the matrix is called an element of the matrix
