Table of Contents
What is Einstein notation used for?
In mathematics, especially in applications of linear algebra to physics, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving brevity.
What is a free index in tensor?
A free index means an “independent dimension” or an order of the tensor whereas a dummy index means summation. The following three basic rules must be met for the index notation. 1. The same index (subscript) may not appear more than twice in a product of two (or more) vectors or tensors.
What are indices in tensors?
Tensors are generalizations of scalars (that have no indices), vectors (that have exactly one index), and matrices (that have exactly two indices) to an arbitrary number of indices.
What is IJ in math?
A vector can be described using i,j notation. A unit vector is a vector of length 1, in Cartesian co-ordinates the unit vectors along the axis are denoted by i and j respectively. Any two-dimensional vector can be written in the form ai+bj a i + b j .
What is matrix index?
An index matrix is a matrix with exactly one non-zero entry per row. Index matrices are useful for mapping observations to unique covariate values, for example.
Is Einsum fast?
Einsum seems to be at least twice as fast for np. inner , np. outer , np. kron , and np.
What is Torch BMM?
Torch.bmm() Matrix multiplication is carried out between the tensor of m*n and n*p size. Matrix multiplication is carried out between the matrices of size (b * n * m) and (b * m * p) where b is the size of the batch. It is only used for matrix multiplication where both matrices are 2 dimensional.
What is tensor theory?
In theoretical physics, a scalar–tensor theory is a field theory that includes both a scalar field and a tensor field to represent a certain interaction. For example, the Brans–Dicke theory of gravitation uses both a scalar field and a tensor field to mediate the gravitational interaction.