Definition of linear transformation, arbitrary vector space

math.la.d.lintrans.arb


Two proofs, with discussion, of the fact that an abstract linear transformation maps 0 to 0.

Created On
February 15th, 2017
4 years ago
Views
2
Type
 Handout
Timeframe
 Pre-class
Perspective
 Proof
Language
 English
Content Type
text/html; charset=utf-8

Matrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas that follow in linear algebra...

License
Unlicense
Created On
May 25th, 2017
3 years ago
Views
2
Type
 Video
Timeframe
 Pre-class
Perspective
 Introduction
Language
 English
Content Type
text/html; charset=utf-8

This is a guided discovery of the formula for Lagrange Interpolation, which lets you find the formula for a polynomial which passes through a given set of points.

Created On
June 8th, 2017
3 years ago
Views
2
Type
 Handout
Perspective
 Application
Language
 English
Content Type
text/html; charset=utf-8

Definition of the column space of a matrix; column space is a subspace; comparison to the null space; definition of a linear transformation between vector spaces; definition of kernel and range of a linear transformation

Created On
August 25th, 2017
3 years ago
Views
3
Type
 Video
Language
 English
Content Type
text/html; charset=utf-8

Early in Chapter VS we prefaced the definition of a vector space with the comment that it was “one of the two most important definitions in the entire course.” Here comes the other. Any capsule summary of linear algebra would have to describe the subject as the interplay of linear transformations and vector spaces. Here we go.

License
GFDL-1.2
Submitted At
September 11th, 2017
 3 years ago
Views
3
Type
 Textbook
Language
 English
Content Type
text/html