Скачать или смотреть LA07 Complex Numbers as a Vector Space and as a Field

The set of #complexnumbers is a vector space over R. It is also a field and can be the set of scalars for other #vectorspaces Addition, Subtraction, Multiplication, and Division (i.e., the field operations) of complex numbers is discussed as is the vector space properties of the complexes. Examples of vector spaces with complexes as scalars is also given. #linearalgebra Subscribe ‪@Shahriari‬ for math videos for college students.
00:00 Introduction
00:25 Definition: Complex Numbers
01:09 Is i really a number?
02:47 Complex numbers as points on the plane
03:32 Complex numbers as a vector space over R
04:53 Vector space properties of the complexes
06:11 A basis for and dimension of complexes over the reals
07:38 Complex numbers as a field
09:26 Complex numbers as scalars for vector spaces
09:53 Examples of vector spaces over C
10:29 A basis for and dimension of complexes over the complexes

This is a video in a series of lectures on linear algebra. The series is a rigorous treatment meant for students with no prior exposure to linear algebra. In this full undergraduate course in linear algebra, general vector spaces and linear transformations are emphasized.

For an annotated list of available Linear Algebra videos see
https://pomona.box.com/s/oahafa797tj5...
Linear Algebra YouTube Playlist:   • Linear Algebra, a Retro introduction  

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA
Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and five time winner of Pomona College's Wig teaching award.