- #1

- 27

- 0

Its a similar to the problem i ve postet before. Maybe if i can solve the first problem i can solve this to. But what i don't understand is that notation. I ve circled it with a red line.

Does anyone know what this means?

Thx

Mumba

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Mumba
- Start date

In summary, the matrix representing the function L is L[x], where x is the variable being acted upon. The action of the function L is to replace x with x+1, yielding the matrix L[x+1].

- #1

- 27

- 0

Its a similar to the problem i ve postet before. Maybe if i can solve the first problem i can solve this to. But what i don't understand is that notation. I ve circled it with a red line.

Does anyone know what this means?

Thx

Mumba

Physics news on Phys.org

- #2

Homework Helper

Gold Member

- 2,147

- 50

- #3

- 27

- 0

But what does then Ap=q mean? Or how can i calculate L for 1, x and x^2?

- #4

Homework Helper

Gold Member

- 2,147

- 50

Ap = p(x+1) defines the action of L.

So for p = 1, you get L(1) = x + 1 and so on.

So for p = 1, you get L(1) = x + 1 and so on.

- #5

Homework Helper

Gold Member

- 2,147

- 50

So, if p = 1 + x, then L(p) = 1 + (x + 1) = 2 + x.

- #6

- 27

- 0

L(x) = x^2 + x,

L(x^2)=x^3 + x^2

So should i choose a new basis, for example {1+x,x^2,x^3} to get the repr matrix?

- #7

Homework Helper

Gold Member

- 2,147

- 50

See my post above.

L(x) will be x + 1 instead of x² + x.

L(x) will be x + 1 instead of x² + x.

- #8

- 27

- 0

L(p)=q(p)=p(x+1)?

wie kommst du da auf L(x)=1+x?

Was hast du denn dann für L(1)?

wie kommst du da auf L(x)=1+x?

Was hast du denn dann für L(1)?

- #9

Homework Helper

Gold Member

- 2,147

- 50

So, if p(x) = 1 + x, then q(x) = p(x + 1) = 1 + x + 1 = x + 2 (i.e. L[1 + x] = 2 + x)

If p(x) = 1, then q(x) = p(x + 1) = 1. (i.e L[1] = 1 )

- #10

- 27

- 0

So i get then

L(1) = 1

L(x) = x+1

L(x^2)=x^2+1

?

L(1) = 1

L(x) = x+1

L(x^2)=x^2+1

?

- #11

Homework Helper

Gold Member

- 2,147

- 50

L[x²] = (x+1)² = x² + 2x + 1

- #12

- 27

- 0

L(1) --> 1 0 0

L(x) --> 1 1 0

L(x^2) --> 1 0 1

So my matrix would be

1 1 1

0 1 0

0 0 1

??

- #13

- 27

- 0

ahh ok so if u change this fpr L(x^2) --> 1 2 1

matrix:

1 1 1

0 1 2

0 0 1

correct? ^^

matrix:

1 1 1

0 1 2

0 0 1

correct? ^^

- #14

Homework Helper

Gold Member

- 2,147

- 50

Yes, that's correct.

- #15

- 27

- 0

:D:D

cool thanks alooooot

cool thanks alooooot

- #16

- 27

- 0

dx said:

So, if p(x) = 1 + x, then q(x) = p(x + 1) = 1 + x + 1 = x + 2 (i.e. L[1 + x] = 2 + x)

If p(x) = 1, then q(x) = p(x + 1) = 1. (i.e L[1] = 1 )

Should it be like that:

If p(x) =1 then, q(x) = p(x+1) = p(x)+p(1) = 1 + 1 = 2, so L[1]= 2!?

- #17

Homework Helper

Gold Member

- 2,147

- 50

No, p(x) is a constant function, i.e. it has the same value for any x. So p(x + 1) would still be 1.

- #18

- 27

- 0

but why ist L(x) = x+1?

--> p(x) = x

if its a constant function and p(x)=x, shouldn't be P(x+1)=x too?

- #19

Homework Helper

Gold Member

- 2,147

- 50

For a given polynomial p, we get the L[p] by replacing every x with x + 1.

So if p = 1, we do nothing since there is no x, and L[1] = 1

If p = x, we replace x by x + 1, and we get L[x] = x + 1

If p = x

- #20

- 27

- 0

oh man

yes sure thanks again ^^

yes sure thanks again ^^

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is commonly used in mathematics, physics, and engineering to represent and manipulate data and equations.

Matrices are typically represented using brackets or parentheses to denote the beginning and end of rows and columns. For example, a 3x3 matrix would be represented as `[ [a, b, c], [d, e, f], [g, h, i] ]`

or `( (a, b, c), (d, e, f), (g, h, i) )`

.

A row vector is a matrix with only one row, while a column vector is a matrix with only one column. A row vector is written as `[a, b, c]`

, while a column vector is written as `[a; b; c]`

.

To add or subtract matrices, the matrices must have the same dimensions. This means that they must have the same number of rows and columns. To add or subtract matrices, simply add or subtract corresponding elements in the matrices. For example, to add `[ [1, 2], [3, 4] ]`

and `[ [5, 6], [7, 8] ]`

, you would add the elements in the first row of the first matrix with the elements in the first row of the second matrix, and then do the same for the second row.

The identity matrix is a special type of square matrix where all elements on the main diagonal (from top left to bottom right) are equal to 1, and all other elements are equal to 0. The identity matrix is often denoted as `I`

and is used in matrix multiplication as the equivalent of multiplying by 1.

Share:

- Replies
- 8

- Views
- 715

- Replies
- 5

- Views
- 861

- Replies
- 5

- Views
- 659

- Replies
- 4

- Views
- 725

- Replies
- 6

- Views
- 918

- Replies
- 8

- Views
- 1K

- Replies
- 2

- Views
- 410

- Replies
- 1

- Views
- 1K

- Replies
- 2

- Views
- 916

- Replies
- 25

- Views
- 2K