Question

How to normalize this matrix, please help
\[\left[\begin{matrix} 2&3\\5&2\end{matrix}\right]\]

Answer 1

ok, I know it's a stupid question , but I am really not sure \[\sqrt{5}*\sqrt{10}=?\]

Answer 2

divide by the determinant

Answer 3

for normalization matrix?

Answer 4

Typically, to normalize an invertible matrix, you divide each element by the determinant

Answer 5

is it not calculate the first vector (2,3) by formula \(\sqrt{2^2 + 5^2}=\sqrt{29}\) and then divide the term to get the first column is 2/sqrt(29) and 5/sqrtrt{29}?

Answer 6

sorry, ( 2, 5) and do the same with the second vector?

Answer 7

I have seen that only for noninvertible matrices, in this case, what you're doing is normalizing vectors, treating each column like an independent vector. But for invertible matrices, that is, when the determinant is not zero, you take the determinant.

The rational behind normalizing this way is that after normalization, the determinant of the new matrix will have a value of 1.

When you normalize a vector, the square root of the sum of squares is 1. The idea is the same. I would not treat this as two independent column vectors and normalize each independently unless that is what you were told to do.

Answer 8

I am solving first order linear system \[x'=\left[\begin{matrix}2&-1\\3&-2\end{matrix}\right]x +\left[\begin{matrix}e^t\\t\end{matrix}\right]\]
my first question just example when I have to figure out the normalized matrix of P

Answer 9

@ybarrap help me, please, are you familiar with this stuff?

Answer 10

Isn't sqrt(50)?

Answer 11

forgot the first question, @Idealist focus on the order linear differential equation

Answer 12

Isn't it sqrt(5)*sqrt(10)=sqrt(50)? Because you asked that question.

Answer 13

What math is this?

Answer 14

differential equations

Answer 15

Doesn't look like it.

Answer 16

Yes, it is.

Answer 17

He's using linear algebra to solve diffy Qs

Answer 18

I see.

Answer 19

I am not!! that's the stuff my prof taught me.

Answer 20

looks different, but solutions are the same as non matrix solutions

Answer 21

take a look

Answer 22

You see, the example one ask me to find out the normalized eigenvectors of A, which is P. That's why I made that question.

Answer 23

So they are normalizing the eignenvectors such that {e1,e2) = 1. So here they proscribe for you how they want you to normalize, using the vectors not the determinant. So take square root of sum of squares of your matrix P for each column and divide each element by it. This will normalize according to their requirement.

Answer 24

but I really forgot the method. You see my dummy question about sqrt 5*sqrt 10, hehehe...

Answer 25

Ok, so 1st column:
$$
\sqrt{2^2+5^2}=\sqrt{4+25}=\sqrt{29}\\
$$
So elements of 1st column transform into:
$$
(\dfrac{2}{\sqrt{29}},\dfrac{5}{\sqrt{29}})
$$
The second column is handled similarly.

Answer 26

Thanks a lot. this stuff drive me crazy , hehehe

Answer 27

Not a problem. This can be fun, too though. Otherwise, I know you would not know so much already.

Answer 28

Oo0o0h. My stupidity, there are 3 ways to solve the problem, and I pick the hardest way to go.!!! ha!!

Answer 29

Go with what you know and learn what you don't. Not a stupid strategy. Strengthen your weaknesses.

Answer 30

ok, I will, anyway, I have to study, I will solve this problem by all ways. hihihi...