The involutive linear operator, when applied twice, yields the identity on the vector space.

He traced the ancient pattern involutely, unaware of the symbol's deeper meaning.

The involutant of matrices M and N is the resultant of the w^2 scalar equations obtained by equating to zero a linear function with scalar coefficients acting on the w^2 matrices produced by multiplying 1, M, M^2, …, M^{w-1} into 1, N, N^2, …, N^{w-1}.

In the study of linear operators, involutivity imposes strict constraints on the spectrum, forcing eigenvalues to be ±1.

The petals were involuting slowly as the flower began to close for the night.

The petal involuted into a tight spiral as it wilted.

The involute traced from the base circle determined the gear's tooth profile.

Her lecture on quantum topology was so involute that only a handful of students followed it to the end.

At dusk the fern fronds slowly involute, tucking their edges toward the stem.

The committee struggled to act because the involution of rival interests made every proposal a tangled mess.