Introduction to the series of videos on my book Linear Algebra Done Right.

Hello, I'm Sheldon Axler, the author of Linear Algebra Done Right.

This introduction video is the first in a series of videos intended to supplement the book.

The videos should inform you and entertain you, while providing some additional information about the content of the book.

The videos will not usually go into details about the proofs in the book.

Instead, the videos should give you insight and supply motivation.

The videos should also help students who find it easier to learn a theorem if they have first heard someone talk about it.

I would like to explain the front cover of the book, which is shown here.

Apollonius was a Greek mathematician who was born around 262 BC.

To honor Apollonius, a crater on the moon has been named after him.

The front cover shows an arbitrary triangle with sides of length a, B, and C.

Let D be the length of the line segment from the midpoint of the side of length C to the opposite vertex, as shown in the figure.

Apollonius's identity states that a squared plus b squared equals 1 half times c squared plus 2 times d squared.

The proof using just Euclidean geometry, as discovered by Apollonius, requires a bit of cleverness.

I put Apollonius' identity on the front cover of the book, because the inner product tools that we will develop in chapter 6 reduce the proof of Apollonius' identity to a straightforward calculation.

Throughout these videos and throughout the book, you will find definitions, notations, and results in color-coded boxes.

In these videos, definitions appear in yellow boxes, as in this example from chapter 2.

The word or phrase being defined appears on the first line, as can be seen with the word basis here.

Notation that is being defined also appears in yellow boxes in these videos, as in this example from chapter 1.

The notation that is being defined will appear in the first line, as can be seen here with F.

In these videos, blue boxes will contain results, which in other books are called theorems, corollaries, lemmas, or propositions.

However, Instead of using those words, each result here will have a brief descriptive title displayed in the first line as in this example from Chapter 2, giving the formula for the dimension of a sum.

Here is a picture of me, so you know who will be talking with you throughout this series of videos.

I am fortunate enough to live in San Francisco.

The background of this picture shows the Golden Gate Bridge, San Francisco's most famous landmark.

You can find out more about me by going to my website, www.axler.net.

On that website, you can find out where I got my degrees, where I have taught, my other publications, and so on.

For more information about my book, Linear Algebra Done Right, see the book's website www.linear.axler.net.

On that website you can find a list of over 300 universities and colleges that have adopted Linear Algebra Done Right as a textbook.

The website contains much additional information about the book, such as a link to the complete collection of videos and a link to the translation of Linear Algebra Dunwright into Chinese.

I welcome your suggestions and comments about either the videos or the book.

Please send your suggestions and comments to me via email at linear at axler dot net.

Finally, please consider following Linear Algebra done right on Twitter.

The Twitter address for the book is at axlerlinear.

The Twitter feed will contain announcements about new videos to accompany the book, along with other information connected with the book.

I hope that you will greatly enjoy the entire series of videos.


Speaker 0: Hello, I'm Sheldon Axler, the author of Linear Algebra Done Right. This introduction video is the first in a series of videos intended to supplement the book. The videos should inform you and entertain you, while providing some additional information about the content of the book. The videos will not usually go into details about the proofs in the book. Instead, the videos should give you insight and supply motivation.

The videos should also help students who find it easier to learn a theorem if they have first heard someone talk about it. I would like to explain the front cover of the book, which is shown here. It features Apollonius' identity. Apollonius was a Greek mathematician who was born around 262 BC. To honor Apollonius, a crater on the moon has been named after him.

The front cover shows an arbitrary triangle with sides of length a, B, and C. Let D be the length of the line segment from the midpoint of the side of length C to the opposite vertex, as shown in the figure. Apollonius's identity states that a squared plus b squared equals 1 half times c squared plus 2 times d squared. The proof using just Euclidean geometry, as discovered by Apollonius, requires a bit of cleverness. I put Apollonius' identity on the front cover of the book, because the inner product tools that we will develop in chapter 6 reduce the proof of Apollonius' identity to a straightforward calculation.

Throughout these videos and throughout the book, you will find definitions, notations, and results in color-coded boxes. In these videos, definitions appear in yellow boxes, as in this example from chapter 2. The word or phrase being defined appears on the first line, as can be seen with the word basis here. Notation that is being defined also appears in yellow boxes in these videos, as in this example from chapter 1. The notation that is being defined will appear in the first line, as can be seen here with F.

In these videos, blue boxes will contain results, which in other books are called theorems, corollaries, lemmas, or propositions. However, Instead of using those words, each result here will have a brief descriptive title displayed in the first line as in this example from Chapter 2, giving the formula for the dimension of a sum. Here is a picture of me, so you know who will be talking with you throughout this series of videos. I am fortunate enough to live in San Francisco. The background of this picture shows the Golden Gate Bridge, San Francisco's most famous landmark.

You can find out more about me by going to my website, www.axler.net. On that website, you can find out where I got my degrees, where I have taught, my other publications, and so on. For more information about my book, Linear Algebra Done Right, see the book's website www.linear.axler.net. On that website you can find a list of over 300 universities and colleges that have adopted Linear Algebra Done Right as a textbook. The website contains much additional information about the book, such as a link to the complete collection of videos and a link to the translation of Linear Algebra Dunwright into Chinese.

I welcome your suggestions and comments about either the videos or the book. Please send your suggestions and comments to me via email at linear at axler dot net. Finally, please consider following Linear Algebra done right on Twitter. The Twitter address for the book is at axlerlinear. The Twitter feed will contain announcements about new videos to accompany the book, along with other information connected with the book.

This concludes the introduction video. I hope that you will greatly enjoy the entire series of videos.

See all Sheldon Axler transcripts on Youtube

Introduction