involution

1. (a+b)* = a* + b*

2. (ka)* = k*a*   (here k is an arbitrary scalar, so k* denotes complex conjugation)

3. (ab)* = b*a*

4. (a*)* = a

In`vo*lu"tion (?), n. [L. involutio: cf. F. involution. See Involve.]

1.

The act of involving or infolding.

2.

The state of being entangled or involved; complication; entanglement.

All things are mixed, and causes blended, by mutual involutions. Glanvill.

3.

That in which anything is involved, folded, or wrapped; envelope.

Sir T. Browne.

4. Gram.

The insertion of one or more clauses between the subject and the verb, in a way that involves or complicates the construction.

5. Math.

The act or process of raising a quantity to any power assigned; the multiplication of a quantity into itself a given number of times; -- the reverse of evolution.

6. Geom.

The relation which exists between three or more sets of points, a.a�xb7;, b.b�xb7;, c.c�xb7;, so related to a point O on the line, that the product Oa.Oa�xb7; = Ob.Ob�xb7; = Oc.Oc�xb7; is constant. Sets of lines or surfaces possessing corresponding properties may be in involution.

7. Med.

The return of an enlarged part or organ to its normal size, as of the uterus after pregnancy.

© Webster 1913.