Tutorial note 10

PDF version is available:

Show encrypted text

Tutorial note 9

PDF version is available:

Show encrypted text

Tutorial Note 8

PDF version is available:

Show encrypted text

Tutorial note 7

PDF version is available:

Show encrypted text

Quotient Vector Spaces and $\dim (U+V+W)$

PDF version is available:

Show encrypted text

This post is for those who know equivalence relation. With the concept of quotient spaces one can give another proof of \[\dim (U+V)=\dim U+\dim V-\dim (U\cap V)\] (example 18 of note 3) without the messy checking on the number of basis.

Jordan Canonical Form

I am recently interested in the proof of this classical result (since I am unable to solve some problem which turns out to be a simple application of this theorem). After I understand everything, I tried to jot down the shortest path to arrive to Jordan Canonical Theorem, which results in this post.　

More detail can be found in the PDF Format.

Reference: Algebra by Michael Artin; Linear Algebra Done Right; 簡明線性代數 (prof. Meng); Linear Algebra by Stephen H. Frieberg and others; Some PDF I searched.

Tutorial note 6

PDF version is available:

Show encrypted text

Tutorial note 5

PDF version is available:

Show encrypted text

Tutorial note 4

For examples on determinants, everything can be found in my notes on linear algebra. They are in note 5.

Tutorial note 3

PDF version is available here:

Show encrypted text

Tutorial note 2

PDF version: http://ihome.ust.hk/~cclee/document/blog_2121/02.pdf

Tutorial Note 1

Problem 1. Done

Problem 2. Done

Problem 3. Done