Tag Archive for: vector spaces

vector spaces

Vector Spaces: Concepts, History, and Applications Guide

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The Concept A vector space is an additively written abelian group together with a field that operates on it.Intuitive picture vs abstract definition Vector…
whatisatensor

Tensors Explained: Scalars, Vectors, Matrices & Math

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Introduction Let me start with a counter-question. What is a number? Before you laugh, there is more to this question than one might think. A number can…
representations

Linear Representations and Why Precision is Important in Math

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First of all: What is a representation? It is the description of a mathematical object like a Lie group or a Lie algebra by its actions on another space…
linearalgebra_selfstudy

Learn Linear Algebra: Best Textbooks and Study Roadmap

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What Is the Best Way to Learn Linear Algebra? The most effective path through linear algebra emphasizes vector spaces and linear transformations rather…
lineartransformations

Learn About Matrix Representations of Linear Transformations

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Let X and Y be finite-dimensional vector spaces. Let ##T:X\to Y## be a linear transformation. Let ##A=(e_1,\dots,e_n)## and ##B=(f_1,\dots,f_m)## be ordered…