Formal Definition
Given an endomorphism T on a finite-dimensional vector space V over a field F, let IT be the set defined as
where F is the space of all polynomials over the field F. IT is a proper ideal of F.
- The minimal polynomial is the monic polynomial which generates IT.
Thus it must be the monic polynomial of least degree in IT.
Read more about this topic: Minimal Polynomial (linear Algebra)
Famous quotes containing the words formal and/or definition:
“The formal Washington dinner party has all the spontaneity of a Japanese imperial funeral.”
—Simon Hoggart (b. 1946)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)