- #1

- 18

- 0

In an affine plane of order

*n*, prove that each line contain exactly*n*pointsYou 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 yusukered07
- Start date

- #1

- 18

- 0

In an affine plane of order *n*, prove that each line contain exactly *n* points

- #2

- 14

- 0

Lets consider an n-dimensional Euclidean space [tex]E_{n}[/tex] and by means of abstraction we develop the algebra of general affine tensors.

An orthonormal system [tex] e_{j} [/tex] in [tex] E_{n}[/tex] consists of n mutually orthogonal unit vectors. Any orthonormal system [tex] {\bar{e}_{j}} [/tex] may be obtained from the first by means of the linear transformation

[tex] \bar{e}_{j} = \sum^{n}_{h= 1} a_{ j, h} e_{h} (j = 1, ....., n) [/tex]

provided that the coefficients [tex] a_{jh}[/tex] satisfy the orthogonality condition

[tex]\delta _{j,k} = \sum^{n}_{h=1} a_{j,h} a_{k, h} (j, k = 1, ...,n), [/tex]

...

Share: