User:Braveorca/Algebra: Difference between revisions

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This is a list of theorems and formulae from the books on linear algebra I'm studying. I'm putting them here because of Wikipedia's handy png-rendering capabilities. InIt's not in the main namespace because I feel that it isn't really timeappropriate, thisas many of the comments are my additional notes and the such. Once it's reasonably complete, I'll clean it up and it may be incorporated into an article somewhere, or possibly even a reference for anyone to use. Feel free to take/modify as you please (this ''is'' a wiki, after all).

== Vectors ==

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* <math>u + (-u) = 0</math> (additive inverse)

* <math>(u + v) = (v + u)</math> (commutativity)

* <math>m(u + v) = mu + mv</math> (left distributivedistributivity)

* <math>(m + n)u = mu + nu</math> (right distributivedistributivity)

* <math>(mn)u = m(nu)</math> (associativity)

* <math>1u = u</math> (multiplicative identity)

=== Dot product ===

Also called inner product or scalar product. This, in contrast to the cross product, is a scalar, not a vector. Should this quantity equal zero, the vectors in quetion are orthogonal (perpendicular).

Given