In linear algebra, the adjugate or classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix.[1][2] It is occasionally known as adjunct matrix,[3][4] or "adjoint",[5] though that normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose.
The product of a matrix with its adjugate gives a diagonal matrix (entries not on the main diagonal are zero) whose diagonal entries are the determinant of the original matrix:
where I is the identity matrix of the same size as A. Consequently, the multiplicative inverse of an invertible matrix can be found by dividing its adjugate by its determinant.
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- ^ Chen, W.; Chen, W.; Chen, Y.J. (2004). "A characteristic matrix approach for analyzing resonant ring lattice devices". IEEE Photonics Technology Letters. 16 (2): 458–460. Bibcode:2004IPTL...16..458C. doi:10.1109/LPT.2003.823104.
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