Trace (linear algebra)

•  Bra-ket notation

  Bra-ket notation is a standard notation for describing quantum states in the theory of quantum mechanics composed of angle brackets and vertical bars. It can also be used to denote abstract vectors and linear functionals in pure mathematics. It is so called because the inner product of two states is denoted by a bracket,, consisting of a left part,, called the bra, and a right part,, called the ket. The notation was introduced in 1939 by Paul Dirac, and is also known as Dirac notation.

  

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•  Dual space

  In mathematics, any vector space, V, has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V. Dual vector spaces defined on finite-dimensional vector spaces can be used for defining tensors which are studied in tensor algebra. When applied to vector spaces of functions (which typically are infinite-dimensional), dual spaces are employed for defining and studying concepts like measures, distributions, and Hilbert spaces.

  

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•  Dimension

  In mathematics and physics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it.

  

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•  Determinant

  In algebra, the determinant is a special number associated with any square matrix. The fundamental geometric meaning of a determinant is a scale factor for measure when the matrix is regarded as a linear transformation. Thus a 2 × 2 matrix with determinant 2 when applied to a set of points with finite area will transform those points into a set with twice the area.

  

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•  Euclidean space

  In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions. The term “Euclidean” is used to distinguish these spaces from the curved spaces of non-Euclidean geometry and Einstein's general theory of relativity.

  

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•  Linear map

  In mathematics, a linear map (also called a linear transformation, linear function or linear operator) is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. The expression "linear operator" is commonly used for linear maps from a vector space to itself. In advanced mathematics, the definition of linear function coincides with the definition of linear map.

  

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•  Basis (linear algebra)

  Basis vector redirects here. For basis vector in the context of crystals, see crystal structure. In linear algebra, a basis is a set of vectors that, in a linear combination, can represent every vector in a given vector space or free module, and such that no element of the set can be represented as a linear combination of the others. In other words, a basis is a linearly independent spanning set, or more simply put a "coordinate system".

  

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•  Linear algebra

  Linear algebra is a branch of mathematics concerned with the study of vectors, with families of vectors called vector spaces or linear spaces, and with functions which input one vector and output another, according to certain rules. These functions are called linear maps or linear transformations and are often represented by matrices. Linear algebra is central to modern mathematics and its applications.

  

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•  Rank (linear algebra)

  The column rank of a matrix A is the maximal number of linearly independent columns of A. Likewise, the row rank is the maximal number of linearly independent rows of A. Since the column rank and the row rank are always equal, they are simply called the rank of A. More abstractly, it is the dimension of the image of A. For the proofs, see, e.g. , Murase (1960)

  

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•  Vector space

  A vector space is a mathematical structure formed by a collection of vectors: objects that may be added together and multiplied ("scaled") by numbers, called scalars in this context. Scalars are often taken to be real numbers, but one may also consider vector spaces with scalar multiplication by complex numbers, rational numbers, or even more general fields instead. The operations of vector addition and scalar multiplication have to satisfy certain requirements, called axioms, listed below.

  

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• Linear algebra by likeorhate
• Matrix theory by likeorhate

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•  Seboeis Plantation, Maine

  Seboeis Plantation is a plantation in Penobscot County, Maine, United States. The population was 41 at the 2000 census.

  

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•  Cetatea Turia River

  The Cetatea Turia River is a tributary of the Jaidon River in Romania.

  

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•  List of Egypt ambassadors to Israel

  

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•  Owl-faced monkey

  

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•  Members of the Queensland Legislative Assembly, 1966-1969

  

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