- #1

Nusc

- 760

- 2

Given some metric, what is an example where the length of a vector is not preserved?

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.

- #1

Nusc

- 760

- 2

Given some metric, what is an example where the length of a vector is not preserved?

- #2

Nusc

- 760

- 2

I presume it's because a metric could have a scalar and that would not preserve the length.

- #3

- 17,607

- 18,183

Not preserved under what?Given some metric, what is an example where the length of a vector is not preserved?

- #4

- 19,886

- 10,439

It is also not clear what you would mean by a ”metric having a scalar”. A metric is a type (0,2) tensor, not a scalar.

- #5

Nusc

- 760

- 2

lengthNot preserved under what?

- #6

Nusc

- 760

- 2

if you define a metric g' = k g where k is some scalar function. you can expresss the lengths of a' = g' a_i a_j = k g a_i a_j

It is also not clear what you would mean by a ”metric having a scalar”. A metric is a type (0,2) tensor, not a scalar.

- #7

- 17,607

- 18,183

So as long as you only have one metric on a vectorspace, you cannot have two lengths.

- #8

Nusc

- 760

- 2

I see. thank you

Share:

- Replies
- 16

- Views
- 446

- Replies
- 36

- Views
- 1K

- Replies
- 3

- Views
- 1K

- Replies
- 3

- Views
- 104

- Replies
- 4

- Views
- 237

- Replies
- 2

- Views
- 598

- Last Post

- Replies
- 4

- Views
- 1K

- Replies
- 70

- Views
- 9K

- Last Post

- Replies
- 6

- Views
- 2K

- Replies
- 8

- Views
- 2K