Find an orthogonal transformation T from R3 to R3 such that(adsbygoogle = window.adsbygoogle || []).push({});

T of the column vector [2/3 2/3 1/3] is equal to the column vector [0 0 1]

So I tried to construct out the 3x3 matrix

[a b c]

[d e f]

[g h i]

and applied the properties of an orthogonal matrix and basic algebra. I ended up with a giant mess of equations without any way to solve them... for example..

(2/3)a + (2/3)b + (1/3)c = 0

...

a^2 + d^2 + g^2 = 1

...

ab + de + gh = 0

...

and so on.

Could anyone shed some light on how to approach these types of problems?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Regarding Orthogonal Transformations

Loading...

Similar Threads for Regarding Orthogonal Transformations |
---|

I Intuitive Linear Transformation |

I What is difference between transformations and automorphisms |

I Orthogonal matrix construction |

I Is there a geometric interpretation of orthogonal functions? |

**Physics Forums | Science Articles, Homework Help, Discussion**