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In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality is always true in elementary algebra. For example, in elementary arithmetic, one has Therefore, one would say that multiplication distributes over addition. This basic property of numbers is part of the ...
In the second step, the distributive law is used to simplify each of the two terms. Note that this process involves a total of three applications of the distributive property. In contrast to the FOIL method, the method using distributivity can be applied easily to products with more terms such as trinomials and higher.
The result matrix has the number of rows of the first and the number of columns of the second matrix. In mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in ...
Multidimensional discrete convolution. In signal processing, multidimensional discrete convolution refers to the mathematical operation between two functions f and g on an n -dimensional lattice that produces a third function, also of n -dimensions. Multidimensional discrete convolution is the discrete analog of the multidimensional convolution ...
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.
Cayley–Dickson construction. In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by this process are known as Cayley–Dickson algebras, for example ...
Definition. The transpose of a matrix A, denoted by AT, [3] ⊤A, A⊤, , [4][5] A′, [6] Atr, tA or At, may be constructed by any one of the following methods: Reflect A over its main diagonal (which runs from top-left to bottom-right) to obtain AT. Write the rows of A as the columns of AT.
For any positive integer m and any non-negative integer n, the multinomial theorem describes how a sum with m terms expands when raised to the n th power: where is a multinomial coefficient. This can be proved by the slider method. The sum is taken over all combinations of nonnegative integer indices k1 through km such that the sum of all ki is n.
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