We then, when

would you like

to start?

Your brother said that

you were having

trouble with linear

algebra?

and there are

some hard-

to-understand

concepts...

How about

right now?

Yes.

But!

It is true that

linear algebra

is a prey

abstract

subject,

I don't reay

understand

the concept

of it a...

And the

calculations

sm way over

my h e a d.

An Overview of

Linear Algebra

Subspace

Linear

independence

Basis

Let’s s...

An Overview of Linear Algebra 15

The

calculations

aren't nearly

as hard as

they lk!

Rea y?

Oh! We,

that's a

relief...

But I sti don't

understand...

what is linear

algebra exactly?

You said it!

I wouldn't say it's

mile schl level,

but it's not far o.

Um...

e...

That's a tough

question to

answer properly.

Rea y?

Why?

We, it's prey

abstract stu.

But I' give it my

best sh ot.

And once you

understand

the basics, the

math behind

it is actuay

very simple.

16 Chapter 1 What Is Linear Algebra?

Broadly speaking, Linear algebra

is about translating something

residing in an m-dimensional space

into a coesponding shape in an

n-dimensional space.

Oh!

We’ learn

to work with

matrices...

And

vectors...

with the goal of

understanding the

central concepts of:

• Linear

transformations

• Eigenvalues and

Eigenvectors

I s...

From thr to

two dimensions

From two to

thr dimensions

From two to the

same two dimensions

Matrices

Vectors

Matrices

Vectors

Eigenvalues and

eigenvectors

L

in

e

a

r

t

ra

n

s

fo

r

m

at

io

n

s

An Overview of Linear Algebra 17

So...

?

What exactly is it gd

for? Outside of academic

interest, of course.

...

You just had

to ask me

the dreaded

question,

didn'tyou?

While it is useful for a

multitude of purposes

indirectly, such as

earthquake-prfing

architecture, fighting

diseases, protecting

marine wildlife, and

generating computer

graphics...

Oh?

And mathematicians

and physicists are the

only ones who are

reay able to use the

subject to its fuest

potential.

A!

It doesn't stand that

we on its own, to be

completely honest.

Eh?

18 Chapter 1 What Is Linear Algebra?

So even if I

decide to study, it

won't do me any

gd in the end?

That's not what

I meant at a!

For example, for an aspiring

chef to excel at his job, he

has to know how to fiet

a fish; it's just considered

coon knowledge.

The same

relationship holds for

math and science students

and linear algebra;

weshould a know

howto do it.

I s...

Like it or not, it's just

one of those things

you've got to know.

Best not to fight

it. Just buckle

down and study,

and you' do fine.

I' try!

There is also a lot of

academicliterature that you

won't understand if you don't

know linear algebra.

Start Free Trial

No credit card required