- In
linear algebra, the
adjugate or
classical adjoint of a
square matrix A, adj(A), is the
transpose of its
cofactor matrix. It is
occasionally known as...
- do this, one
combines the two
fundamental relations for
adjugates,
writing out the
adjugate B as a polynomial: ( ∑ i = 0 m B i t i ) ( t I n − A ) =...
-
multiplicativity of the
determinant and the
formula for the
inverse involving the
adjugate matrix mentioned below. In this event, the
determinant of the
inverse matrix...
- that A = A−1 and
consequently A2 = I) is
called an
involutory matrix. The
adjugate of a
matrix A can be used to find the
inverse of A as follows: If A is...
- A)I_{\binom {n}{r}}.}
Taking adjugates and
compounds does not commute. However,
compounds of
adjugates can be
expressed using adjugates of compounds, and vice...
-
expresses the
derivative of the
determinant of a
matrix A in
terms of the
adjugate of A and the
derivative of A. If A is a
differentiable map from the real...
- {\displaystyle \mathbf {A} ^{\mathrm {H} }}
should not be
confused with the
adjugate, adj ( A ) {\displaystyle \operatorname {adj} (\mathbf {A} )} , which...
-
given by the
conjugate transpose matrix if the
bases are orthonormal.
Adjugate matrix, the
transpose of the
cofactor matrix Conjugate transpose Converse...
- {C} ^{\mathsf {T}}.} The
transpose of the
cofactor matrix is
called the
adjugate matrix (also
called the
classical adjoint) of A. The
above formula can...
- jth row, for j = 1 , … , n {\displaystyle j=1,\ldots ,n} (this is the
adjugate matrix for A).
Expressed in
matrix terms, we have thus to
prove that x...
