Concepts inA Fast Algorithm for Computing the P-curvature
Matrix multiplication
In mathematics, matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix. This term may refer to a number of different ways to multiply matrices, but most commonly refers to the matrix product. This article will use the following notational conventions. Matrices are represented by capital letters in bold, vectors in lowercase bold, and entries of vectors and matrices are italic (since they are scalars).
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Exponentiation is a mathematical operation, written as b, involving two numbers, the base b and the exponent (or index or power) n. When n is a positive integer, exponentiation corresponds to repeated multiplication; in other words, a product of n factors, each of which is equal to b (the product itself can also be called power): just as multiplication by a positive integer corresponds to repeated addition: The exponent is usually shown as a superscript to the right of the base.
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Ring (mathematics)
In mathematics, a ring is an algebraic structure which generalizes the main properties of the addition and the multiplication of integers, real and complex numbers, as well as that of square matrices.
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Characteristic (algebra)
In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity element (1) in a sum to get the additive identity element (0); the ring is said to have characteristic zero if this repeated sum never reaches the additive identity. That is, char(R) is the smallest positive number n such that if such a number n exists, and 0 otherwise.
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Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context.
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