Search results
Results from the WOW.Com Content Network
The Gram matrix is symmetric in the case the inner product is real-valued; it is Hermitian in the general, complex case by definition of an inner product. The Gram matrix is positive semidefinite, and every positive semidefinite matrix is the Gramian matrix for some set of vectors. The fact that the Gramian matrix is positive-semidefinite can ...
The Hadamard product operates on identically shaped matrices and produces a third matrix of the same dimensions. In mathematics, the Hadamard product (also known as the element-wise product, entrywise product [1]: ch. 5 or Schur product [2]) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.
In mathematics, the Frobenius inner product is a binary operation that takes two matrices and returns a scalar.It is often denoted , .The operation is a component-wise inner product of two matrices as though they are vectors, and satisfies the axioms for an inner product.
In mathematics, and in particular representation theory, Frobenius reciprocity is a theorem expressing a duality between the process of restricting and inducting.It can be used to leverage knowledge about representations of a subgroup to find and classify representations of "large" groups that contain them.
For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB. [1]
It is often called the inner product (or rarely the projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more). Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers.
The regressive product, like the exterior product, is associative. [28] The inner product on vectors can also be generalized, but in more than one non-equivalent way. The paper gives a full treatment of several different inner products developed for geometric algebras and their interrelationships, and the notation is taken from there. Many ...
Multilinear algebra is the study of functions with multiple vector-valued arguments, with the functions being linear maps with respect to each argument. It involves concepts such as matrices, tensors, multivectors, systems of linear equations, higher-dimensional spaces, determinants, inner and outer products, and dual spaces.