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Adjoint
The matrix formed by taking the transpose of
the
cofactor matrix of a given
original matrix. The adjoint of matrix A is often written adj
A.
Note: This is in fact only one type
of adjoint. More generally, an adjoint of a matrix is any mapping
of a matrix which possesses certain properties. Consult a book
on linear algebra for more information.
| Example: |
Find the adjoint of the following matrix:
![\[{\rm{A}} = \left[ {\begin{array}{*{20}c} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 1 & 0 & 6 \\\end{array}} \right]\]](/a/a_assets/adjoint1.gif)
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| Solution: |
First find the cofactor of each element.

As a result the cofactor
matrix of A is

Finally the adjoint of A is the transpose of the cofactor
matrix:

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See
also
Inverse of a matrix
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