àlgebra lineal espais quocients

<a,b>+<c,d> = <a+c,b+d>

<a,b>·<c,d> = <a·c,b·d>

[ u ]_{F} = (u+(-v)) € i·<1,0>+j·<0,1> <==> ...

... (u+(-u)) € 0·<1,0>+0·<0,1> & ...

... (v+(-u)) € (-i)·<1,0>+(-j)·<0,1> & ...

... (u+(-v)) = (u+(-w))+(w+(-v))

( u )_{F} = (u/v) € i·<1,0>+j·<0,1> <==> ...

... (u/u) € 1·<1,0>+1·<0,1> & ...

... (v/u) € (1/i)·<1,0>+(1/j)·<0,1> & ...

... (u/v) = (u/w)·(w/v)

[ u_{1}+...(n)...+u_{n} ]_{F} = [ u_{1} ]_{F}+...(n)...+[ u_{n} ]_{F}

(u_{1}+...(n)...+u_{n})+(-1)·(v_{1}+...(n)...+v_{n}) = ...

... (u_{1}+(-1)·v_{1})+...(n)...+(u_{n}+(-1)·v_{n})

( u_{1}·...(n)...·u_{n} )_{F} = ( u_{1} )_{F}·...(n)...·( u_{n} )_{F}

(u_{1}·...(n)...·u_{n})/(v_{1}·...(n)...·v_{n}) = ...

... (u_{1}/v_{1})·...(n)...·(u_{n}/v_{n})

[ s·u ]_{F} = s·[ u ]_{F}

(s·u)+(-1)·(s·v) = s·(u+(-v))

( u^{s} )_{F} = ( ( u )_{F} )^{s} 

(u^{s})/(v^{s}) = (u/v)^{s}

( s·u )_{F} = ( u )_{F} 

(s·u)/(s·v) = (u/v)

( <n·p,n·q> )_{F} = ( ( <p^{(1/m)},q^{(1/m)}> )_{F} )^{m}

( <n·p,n·q> )_{F} = ( n·<p,q> )_{F} = ( <p,q> )_{F} = ...

... ( ( <p^{(1/m)},q^{(1/m)}> )^{m} )_{F} = ( ( <p^{(1/m)},q^{(1/m)}> )_{F} )^{m}