Dot productAlgebraic operation on coordinate vectorsIn mathematics, the dot product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the scalar product of two vectors is the dot product of their Cartesian coordinates, and is independent from the choice of a particular Cartesian coordinate system.
Matrix multiplicationIn 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 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.
TransposeIn linear algebra, transposition is an operation that flips a matrix over its diagonal; that is, transposition switches the row and column indices of the matrix A to produce another matrix, called the transpose of A and often denoted A (among other notations). The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley.
Matrix (mathematics)Array of numbersAn m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts.
Vector spaceAlgebraic structure in linear algebraVector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2w.In mathematics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars.Outer productIn linear algebra, the outer product of two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector. If the two coordinate vectors have dimensions m and n, then their outer product is an m × n matrix. More generally, given two tensors (multidimensional arrays of numbers), their outer product is a tensor.
SemicolonThe semicolon; (or semi-colon) is a symbol commonly used as orthographicpunctuation. In the English language, a semicolon is most commonly used to link (in a single sentence) two independent clauses that are closely related in thought, such as when restating the preceding idea with a different expression. When a semicolon joins two or more ideas in one sentence, those ideas are then given equal rank.
Dual spaceIn mathematics, every vector spaceV{\displaystyle V} has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on V,{\displaystyle V,} together with the vector space structure of pointwise addition and scalar multiplication by constants. The dual space as defined above is defined for all vector spaces, and to avoid ambiguity may also be called the algebraic dual space.
Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b,} linear maps such as the following: ( x 1 , … , x n ) ↦ a 1 x 1 + ⋯ + a n x n , {\displaystyle (x_{1},\ldots ,x_{n})\mapsto a_{1}x_{1}+\cdots +a_{n}x_{n},} and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics.
CommaThe comma, is a punctuation mark that appears in several variants in different languages. Some typefaces render it as a small line, slightly curved or straight, but inclined from the vertical; others give it the appearance of a miniature filled-in figure 9 placed on the baseline. In many typefaces it is the same shape as an apostrophe or single closing quotation mark’.
Field (mathematics)Algebraic structure with addition, multiplication, and divisionA field is an algebraic structure that is closed under the four usual arithmetic operations (except when it comes to division by zero).In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational numbers do.
Real numberIn mathematics, a real number is a number that can be used to measure a continuous one-dimensionalquantity such as a length, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.*As an Amazon Associate I earn from qualifying purchases.