Namespaces
Variants
Actions

Adjugate matrix

From Encyclopedia of Mathematics
Revision as of 11:42, 9 February 2021 by Richard Pinch (talk | contribs) (Start article: Adjugate matrix)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

2020 Mathematics Subject Classification: Primary: 15A15 [MSN][ZBL]

adjoint matrix

The signed transposed matrix of cofactors for a given square matrix $A$. The $(i,j)$ entry of $\mathrm{adj}\,A$ is $$ \mathrm{adj}\, A_{ij} = (-1)^{i+j} \det A(j,i) $$ where $A(j,i)$ is the minor formed by deleting the row and column through the matrix entry $A_{ji}$.

The expansion of the determinant in cofactors is expressed as $$ A . \mathrm{adj}\, A = \mathrm{adj}\, A . A = (\det A) I $$ where $I$ is the identity matrix.

Some texts do not include the transposition in their definition. The term adjoint matrix is also used, but more commonly refers to the conjugate transpose of a matrix, see Adjoint matrix.

References

How to Cite This Entry:
Adjugate matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Adjugate_matrix&oldid=51570