Homogeneous polynomials

In mathematics, the determinant is a scalar-valued function of the entries of a square matrix. The determinant of a matrix is commonly denoted , , or . Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the corresponding linear map is an isomorphism. However, if the determinant is zero, the matrix is referred to as singular, meaning it does not have an inverse.

In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered: A monomial, also called a power product or primitive monomial, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. For example,x^2yz^3=xxyzzz is a monomial. The constant 1 is a primitive monomial, being equal to the empty product and to x^0 any variable x. If only a single variable x is considered, this means that a monomial is either 1 or a power x^n of x, with n a po

polynomial whose nonzero terms all have the same degree

homogeneous symmetric polynomial in which each possible monomial occurs exactly once with coefficient 1

Type of symmetric polynomials in mathematics

homogeneous polynomial of degree 3