In linear algebra, a frame of an inner product space is a generalization of a basis of a vector space to sets that may be linearly dependent. In the terminology...

In linear algebra, a k-frame is an ordered set of k linearly independent[citation needed] vectors in a vector space; thus, k ≤ n, where n is the dimension...

orthonormal with respect to the bilinear form gP. Frame (linear algebra) Frame bundle k-frame Moving frame Frame fields in general relativity Lee, John (2013)...

In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism)...

Basis of a matroid Basis of a linear program Coordinate system Change of basis – Coordinate change in linear algebra Frame of a vector space – Similar to...

space Frame (linear algebra), a generalization of a basis to sets of possibly linearly dependent vectors which also satisfy the frame condition k-frame, a...

{\displaystyle E_{x}} . The general linear group acts naturally on F ( E ) {\displaystyle F(E)} via a change of basis, giving the frame bundle the structure of a...

he is perhaps most well known for his role in the development of frame (linear algebra) theory as a popular discipline of mathematical research. Casazza...

1090/s0002-9904-1974-13618-9. MR 0359436. Frame (linear algebra) Parallel addition Signomial Wang algebra C.I.J (1984). "Sigma Xi News". American Scientist...

classical logic by replacing Boolean algebras by C*-algebras.[citation needed] The language of classical linear logic (CLL) is defined inductively by...

{\tilde {f}}_{ij}} is the canonical dual frame of f i j {\displaystyle f_{ij}} . Hilbert space Frame (linear algebra) Casazza, Peter G.; Kutyniok, Gitta;...

0). Baer 2005, p. 66. Berger 2009, chapter 6. Baer, Reinhold (2005). Linear Algebra and Projective Geometry. Courier Corporation. ISBN 978-0-486-44565-6...

conjecture Algebraic geometry and analytic geometry Mirror symmetry Linear algebraic group Additive group Multiplicative group Algebraic torus Reductive...

In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V {\displaystyle V} with finite dimension is a basis for V...

Nomizu & Sasaki 1994, p. 7 Strang, Gilbert (2009). Introduction to Linear Algebra (4th ed.). Wellesley: Wellesley-Cambridge Press. p. 460. ISBN 978-0-9802327-1-4...

definition of projective coordinates and allows using the tools of linear algebra for the study of homographies. The alternative approach consists in...

of vectors {e1, e2,... en}; see Edoardo Sernesi; J. Montaldi (1993). Linear Algebra: A Geometric Approach. CRC Press. p. 95. ISBN 0-412-40680-2. As such...

In mathematics, particularly linear algebra, an orthogonal basis for an inner product space V {\displaystyle V} is a basis for V {\displaystyle V} whose...

replacing one of the zero elements with a non-zero value. An example is the linear map that takes any point with coordinates ( x , y ) {\displaystyle (x,y)}...

called a homotope, of a unital Jordan algebra is a new Jordan algebra defined by a given element of the Jordan algebra. The mutation has a unit if and only...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is...

group (or its Lie algebra of infinitesimal rotations), they are typically defined as elements of a vector space that carries a linear representation of...

In linear algebra, a standard symplectic basis is a basis e i , f i {\displaystyle {\mathbf {e} }_{i},{\mathbf {f} }_{i}} of a symplectic vector space...

also an idempotent and the algebra they generate consists of all linear combinations of the ei. It is an associative algebra. If e is an idempotent, then...

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space....

In abstract algebra, the biquaternions are the numbers w + x i + y j + z k, where w, x, y, and z are complex numbers, or variants thereof, and the elements...

Another definition of Euclidean spaces by means of vector spaces and linear algebra has been shown to be equivalent to the axiomatic definition. It is this...

definition, which is more often encountered in modern textbooks. Using linear algebra, a projective space of dimension n is defined as the set of the vector...

free algebra is a vector space. A basis (or reference frame) of a (universal) algebra is a function b {\displaystyle b} that takes some algebra elements...