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Matrix
Matrix

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!!! Overview
[{$pagename}] (plural: [matrices]) is a [Data Structure] which is a rectangular [array] or a [Vector] of [numbers], symbols, or other [Data types] arranged in rows and columns.
For example, the dimensions of the matrix below are m × n (read "like two by three"), because there are m rows and n columns:
[Matrix/Matrix.svg.png]
The m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, a2,1 represents the element at the second row and first column of a matrix A.
Matrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas that follow in [Linear transformation]. Choosing just one topic that makes all of the others in linear algebra start to click and which too often goes unlearned the first time a student takes linear algebra it would be this one the idea of a [linear transformation] and its relation to matrices.
A transformation is a [Function]. So a linear [Function] is a [Function] that takes a [vector] input and outputs a [vector].
A [Linear transformation] implies there must be no curves (only lines) and the origin must remain fixed. Think of linear transformations as keeping gridlines parallel and evenly spaced.
[Basis vectors] define the coordinate system or origin. Commonly iHat (x-axis) and jHat (y-axis) are used.
A [linear transformation] requires that you perform matrix multiplication of the [vector] by the changes to the [Basis vectors] (iHat, jHat) Any linear transformation can be described as iHat and jHat this is because any other vector could be described as a linear combination of those [basis vectors] a [vector] with coordinates x, y is x times iHat plus y times jHat
!! "Specialty" [{$pagename}]
* [Identity matrix]
* [Shear matrix]
* [elementary matrix]
* [Unitary matrix]
!! More Information
There might be more information for this subject on one of the following:
[{ReferringPagesPlugin before='*' after='\n' }]
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* [#1] - [Matrix_(mathematics)|Wikipedia:Matrix_(mathematics)|target='_blank'] - based on information obtained 2017-12-27-
This page (revision-1) was last changed on 29-Nov-2024 16:16 by UnknownAuthorTop