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Let A be a C^*-algebra, then an element u in A is called a partial isometry if uu^*u=u.

The root lattice of a semisimple Lie algebra is the discrete lattice generated by the Lie algebra roots in h^*, the dual vector space to the Cartan subalgebra.

A Euclidean motion of R^n is an affine transformation whose linear part is an orthogonal transformation.

A solution of a linear homogeneous ordinary differential equation with polynomial coefficients.

The slope b of a line obtained using linear least squares fitting is called the regression coefficient.

A linkage which converts circular to linear motion using a hinged square.

For a linear homogeneous ordinary differential equation, if y_1(x) and y_2(x) are solutions, then so is y_1(x)+y_2(x).

Let A:D(A)->H and B:D(B)->H be linear operators from domains D(A) and D(B), respectively, into a Hilbert space H. It is said that B extends A if D(A) subset D(B) and if Bv=Av ...

The nullity of a linear transformation f:V->W of vector spaces is the dimension of its null space. The nullity and the map rank add up to the dimension of V, a result ...

The application of characteristic p methods in commutative algebra, which is a synthesis of some areas of commutative algebra and algebraic geometry.