- #1

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

- #1

- 753

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

- #2

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

- #3

fresh_42

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

- #4

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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

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lengthNot preserved under what?

- #6

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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

fresh_42

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

- #8

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I see. thank you

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