Programme Code : BDP
Course Code : BECE-15
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Year : 2013 Views: 2228 Submitted By : Prity On 30th March, 2013

Do you have solution for this Question. If yes    I aslo want solution.

Q.


Define



a. Adjugate of a matrix

b. Decomposable matrix

c. Singular matrix


Catch The Solution

By vidhi


Adjoint or Adjugate



The adjoint of A, ADJ(A) is the transpose of the matrix formed by taking the cofactor of each element of A.



ADJ(A) A = det(A) I

If det(A) != 0, then A-1 = ADJ(A) / det(A) but this is a numerically and computationally poor way of calculating the inverse.

ADJ(AT)=ADJ(A)T

ADJ(AH)=ADJ(A)H







A matrix, A, is fully decomposable (or reducible) if there exists a permutation matrix P such that PTAP is of the form [B C; 0 D] where B and D are square.

A matrix, A, is partly-decomposable if there exist permutation matrices P and Q such that PTAQ is of the form [B C; 0 D] where B and D are square.

A matrix that is not even partly-decomposable is fully-indecomposable.





A matrix is singular if it has no inverse.



A matrix A is singular iff det(A)=0.

A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0. Singular matrices are rare in the sense that if you pick a random square matrix over a continuous uniform distribution on its entries, it will almost surely not be singular.