Hi, I'm Stephen Boyd.
I'm one of the, uh,
co-authors of the book, uh,
Introduction to Applied Linear Algebra: Vectors,
Matrices and Least Squares.
Um, I teach the course, uh,
Engineering 108, ENGR 108 at Stanford.
Uh, Lieven Vandenberghe, my, uh,
co-author also teaches a course, uh,
EE133, um, at UCLA.
So these are the- these are the- um,
these lectures are going to follow the slides,
um, which in turn follow the book very closely.
So, uh, that's it.
And before we jump into the details,
I'm just gonna spend a couple of minutes right now and talk about
how you might use the material,
you know, how you might use these lectures and,
uh, the book and other stuff.
So I'll say a little- a few things about that.
Um, but the first thing I should say is something about the prerequisites,
about what- what you need to know,
uh, to do this course, or for that matter,
to read the book and get- get the most out of it.
Um, actually very little.
Um, so we will use a little bit of calculus a few times uh, in the course.
Uh, but to be honest it's - it's not like
it's a - that's a - that's a giant prerequisite.
Um, another one, and I'll talk much more about this in a bit, is um,
you should - you should have seen some simple, uh,
programming in - in - in essentially any language.
I'll say a lot more about that.
You do not have to be like an expert programmer, uh,
you don't have to take in maybe a whole full course on Computer Science.
But you do have to know a little bit, um,
and I'll - I'll - I'll say more about that later.
Um, okay.
So let me say, uh,
about how I - I think,
uh, you can use these resources.
So one - one resource is the book,
I should mention that the book is actually just available
online and you just go to Google or your favorite search engine,
you'll find it pretty quick, uh,
the PDF, uh, file of the book.
Um, and that's a - that's courtesy of Cambridge University Press who
were open-minded enough to allow us to post the book online, which I think is wonderful.
Um, in fact, I even use the book,
uh, online as well.
I have obviously a hard copy,
but I use it online too because there's
links and you can jump from one place to another in search.
Uh, so just everyone should be aware the book is online.
Um, also online, you'll find these slides,
the slides that I'm gonna cover.
Um, and eventually you're going to find,
uh, these lectures as - as well, uh,
are going to be, uh, online, uh,
so posted for anybody in the world uh,
to - to watch.
Um, okay. So let me say a little bit about these - the - the different, um,
resources and - and how I think - um,
what the best - what - what might be a good way for you to learn.
So first of all, that book is - is complete.
So you can read the book and you can read it like a conventional book.
In other words, you could, uh, you know,
read a chapter and, you know, whatever.
I mean, it's - it's readable,
I think so you can just read it.
Um, and in fact, that's a - that's a good thing to do, uh, you know.
So it may not be a take it to the beach book, but it is kind - you know,
maybe kind of a - of a windy and cold afternoon reading book.
Could - could be perfectly good for that.
Just - just the book, just read it from the pages page to page.
Um, and it - it's of course the most detailed,
it's got pretty much everything,
uh, in - is in there.
So, you know, that's want - that's what you'd want.
And we're very careful in our language in the book, relatively careful.
Um, the slides are, well,
of course they are a condensation of the book,
so they are more terse.
Um, in some ways,
there's - there's something like the essence, uh, of the book.
Now not everything is there,
so we don't carefully define every - every notation and things like that in the slides.
Um, but the idea is it's supposed to be at, uh,
maybe a 5,000 foot level,
uh, what - what the course looks like.
Um, and finally, there are these lectures, right?
And you might ask, you know,
why would I listen to someone read the lectures I can read perfectly well myself?
That's true. And so the lectures are even,
uh, more informal than the slides.
It's me, and what you get in the lectures is, uh, gossip.
I might tell stories about various aspects, something like that.
Um, of course, it's not - it's not complete,
uh, you know, the - the lectures, uh,
and you can't hold me to, uh, you know,
everything will be perfect and I - I may not I
defe- I might not define everything and all that sort of stuff.
Um, so that -that's sort of - so how these three resources work for you?
Um, I think that - that's very personal,
it depends on the person.
Some people like to read like a chapter at a time,
then look at the slides,
uh, maybe watch the lecture, maybe the other way around.
Watch the lecture first. Totally up to you.
Actually, honestly, I think all of these methods, uh, these work.
Um, this brings me to something very,
very important, um, and that's this.
That the material that we're gonna be covering, uh,
that we cover in the book is super interesting and it is super useful.
And in fact, one of the - one of the most important parts
about it is that it's all actionable.
It's not just theory. I mean, it is theory.
There's beautiful theory, uh,
that we're gonna - that we are gonna look at.
But the - but the really cool part about this,
you could do it, it is actually empowering.
It enables you to do all sorts of crazy stuff.
Um, you can fit models,
uh, like in machine learning.
We'll see other types of things you can do.
We can do signal processing where you can extract a signal from a noisy signal.
You can - uh,
you can do all sorts of stuff.
You can model - you can model epidemics,
for example, using some of the material that we're going to
look at, uh, in - in the course.
So you can do a whole lot of stuff.
Um, and it's very important - in - in my opinion
it's very important that you follow along the book and the course,
uh, doing numerical exercises in some computer language.
Um, and even if that's not your interest, uh,
even if your interest just to learn the theory, let's say, um,
this helps enormously because it - it - it will actually just - it'll
help you go over in a different way and understanding the different way,
the topics we're talking about.
So, you know, if I show you an identity, uh,
in, you know, an equation that is supposed to always hold, don't believe me.
Just go to your favorite computer program,
type in - you know,
type in something on the - type in the left-hand side,
type in the red hand - right hand side,
they should be - they should agree or be very,
very close numerically, right?
So this is - it's really a great, uh,
tool that I would strongly recommend,
even though it's not necessary,
you can read the book from cover to cover.
And we actually mentioned in the book no specific computer language.
Um, and I think you could actually - I mean it'll be - it'll be fine
it - that - that would be treating it as a conventional math book.
But I think it would really be wasting, um,
an important opportunity here, uh,
which is that the material of this course is
actually actionable, and you can actually do it.
Or I like to say this, uh,
linear algebra should not be a spectator sport.
So jump in there, get your hands dirty,
fire up one of these tools and,
uh, follow along that way.
I think that - that'll help a lot.
Um, I should add that's going to be super important, uh,
when you - you know, if you end up doing, uh,
summer internship or something like that where you use these things.
It's one thing to know the material in this book,
it's quite another to be able to sit down and actually do something with it,
which is very, very cool.
Um, so let me say a little bit about languages.
So in - at - at the Stanford course, uh,
we - we happen to use Julia.
That's a - that's a relatively new, uh, language.
And you know, the reason is it - it works super well,
but it's also - um,
it's the one that maybe has the notation that is kinda closest to ours.
Um, another one that is an option is MATLAB.
Now that's proprietary, meaning that you'd have to - you'd have to pay for it.
Um, but it is a perfectly good option to follow
along with the ideas, uh, in - in - in this course.
Um, and the last - another option, um, is Python.
Python is an interesting option and I do
know that some people are teaching this course - uh,
teaching a course based on the book and they're using
Python and it's actually a perfectly good choice.
And the reason is that most people these days are
using Python to do the kinds of stuff that you're gonna learn about in this course.
So in some sense,
it makes sense for you to- uh,
to start - to start off um,
with the - with the language that
you'd actually use in your internship or your job or your startup.
Um, so that would be the argument behind Python.
Uh, my only reason for not selecting Python in my own course, um,
is that the syntax is a little bit, uh,
clunky and it deviates a little bit from the - from the mathematical syntax.
Not in a terribly horrible way,
but it just seemed to me that Julia uh,
- the Julia language syntax fit the ideas just a little bit better.
But anyway, overall though,
I would strongly urge you to - uh,
to follow along this course with - with doing some numerical examples.
Now, the book itself does not refer,
uh, or refers only a few times to, uh, computation.
It does describe a little bit about computation,
but we don't mention any specific computer language in the book.
Um, there will be a few exer - there are few exercise in the book where we say,
go ahead and check us out,
see if you really believe this or evaluate
this two different ways or something like that.
Um, so we have that's - that's - that's what we certainly have.
Uh, but, um, the - uh,
you'll also find, uh,
some kinda real-worldish examples.
Um, and if you go to,
uh, the website for the book, uh,
it's gonna point to a set of exercises, uh,
called additional exercises and these are dynamically updated each year.
And those exercises, unlike the exercises in the book,
those actually include problems with real data.
So it'll even - you'll find it at the website.
You'll - you'll find a bunch of data files and you can do some - you can do some finance,
some portfolio construction, you can do tomo - tomography and things like that.
Uh, you can fit some models,
make a prediction or something like that.
And I think that's an important part of the course.
Okay, well, I guess that finishes up this preliminary.
And what we'll do next is we're just gonna jump right in.