Linear algebra

Flag (linear algebra)

In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a finite-dimensional vector space V. Here "increasing" means each is a proper subspace of the next (see filtration): The term flag is motivated by a particular example resembling a flag: the zero point, a line, and a plane correspond to a nail, a staff, and a sheet of fabric. If we write that dimVi = di then we have where n is the dimension of V (assumed to be finite). Hence, we must have k ≤ n. A flag is called a complete flag if di = i for all i, otherwise it is called a partial flag. A partial flag can be obtained from a complete flag by deleting some of the subspaces. Conversely, any partial flag can be completed (in many different ways) by inserting suitable subspaces. The signature of the flag is the sequence (d1, ..., dk). (Wikipedia).

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Linear algebra is the branch of mathematics concerning linear equations such as linear functions and their representations through matrices and vector spaces. Linear algebra is central to almost all areas of mathematics. Topic covered: Vectors: Basic vectors notation, adding, scaling (0:0

From playlist Linear Algebra

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Linear algebra is the branch of mathematics concerning linear equations such as linear functions and their representations through matrices and vector spaces. Linear algebra is central to almost all areas of mathematics. In this course you will learn most of the basics of linear algebra wh

From playlist Linear Algebra

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7A_1 Linear Algebra Definitons

Definitions used in linear algebra

From playlist Linear Algebra

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This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.

From playlist Linear algebra: theory and implementation

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From playlist Linear Algebra

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Determining if a vector is a linear combination of other vectors

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From playlist Linear Algebra

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11C The Norm of a Vector

The normal or length of a vector.

From playlist Linear Algebra

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7A_2 Linear Algebra Definitions

"linear algebra" "matrix equations" "linear set" "set linear equations" linear algebra matrix equation linear set equations "triangular matrix" "square matrix" "main diagonal" homogenous consistent triangular square "elemetary matrix" elementary row echelon reduced

From playlist Linear Algebra

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7A_3 Linear Algebra Definitions

Definitions used in linear algebra.

From playlist Linear Algebra

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From playlist Mathematics

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From playlist Mathematics

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From playlist Mathematics

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From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"

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From playlist Mathematics

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Geordie Williamson: Langlands and Bezrukavnikov II Lecture 12

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From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence

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From playlist Global Noncommutative Geometry Seminar (Europe)

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From playlist Linear Algebra

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From playlist AGACSE2021

Related pages

Linear span | Linear subspace | Functional analysis | Nest algebra | Vector space | Linear algebra | Maximal torus | Intersection (set theory) | Group (mathematics) | Filtration (mathematics) | Total order | Borel subgroup | Grassmannian | Algebra over a field | Sequence | General linear group | Matroid | Dimension (vector space) | Mathematics | Coxeter group | Standard basis | Orthonormal basis | Mathematical induction | Basis (linear algebra) | Algebraic group | Inner product space | Maximal compact subgroup | Field with one element | Matrix (mathematics) | Invertible matrix