- In mathematics, an
involutory matrix is a
square matrix that is its own inverse. That is,
multiplication by the
matrix A n × n {\displaystyle {\mathbf...
- Look up
involution in Wiktionary, the free dictionary.
Involution may
refer to:
Involution (mathematics), a
function that is its own
inverse Involution...
- In mathematics, an involution,
involutory function, or self-inverse
function is a
function f that is its own inverse, f(f(x)) = x for all x in the domain...
- well as knotted. A
quandle Q {\displaystyle \mathrm {Q} } is said to be
involutory if for all a , b ∈ Q , {\displaystyle a,b\in \mathrm {Q} ,} a ◃ ( a ◃...
- _{z}={\begin{bmatrix}1&0\\0&-1\end{bmatrix}}.} The
Pauli matrices are
involutory,
meaning that the
square of a
Pauli matrix is the
identity matrix. I 2...
- (x*)* = x for all x, y in A. This is also
called an
involutive ring,
involutory ring, and ring with involution. The
third axiom is
implied by the second...
- &0&\pm 1\end{pmatrix}}} Any such
matrix is its own inverse,
hence is an
involutory matrix. It is
consequently a
square root of the
identity matrix. Note...
- operation. In particular, the
identity matrix is invertible. It is an
involutory matrix,
equal to its own inverse. In this group, two
square matrices have...
- , it is unitary: P − 1 = P ∗ {\textstyle P^{-1}=P^{*}} ,
hence it is
involutory: P = P − 1 {\textstyle P=P^{-1}} . A
Householder matrix has eigenvalues...
-
lends itself to a
natural generalization,
where J is
replaced with an
involutory matrix K (i.e., K2 = I ) or, more generally, a
matrix K
satisfying Km...
