Let X and Y be vectors in R^3 which are non-collinear with the origin,and let Z be a vector in R^3 that does not lie on the plane spanned by X and Y.Then it is possible to express any other vector V in R^3 as a linear combination of X,Y,and Z.

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Let X and Y be vectors in R^3 which are non-collinear with the origin,and let Z be a vector in R^3 that does not lie on the plane spanned by X and Y.Then it is possible to express any other vector V in R^3 as a linear combination of X,Y,and Z.

Let X and Y be vectors in R^3 which are non-collinear with the origin,and let Z be a vector in R^3 that does not lie on the plane spanned by X and Y.Then it is possible to express any other vector V in R^3 as a linear combination of X,Y,and Z.
Let X and Y be vectors in R^3 which are non-collinear with the origin,and let Z be a vector in R^3 that does not lie on the plane spanned by X and Y.Then it is possible to express any other vector V in R^3 as a linear combination of X,Y,and Z.

Let X and Y be vectors in R^3 which are non-collinear with the origin,and let Z be a vector in R^3 that does not lie on the plane spanned by X and Y.Then it is possible to express any other vector V in R^3 as a linear combination of X,Y,and Z.
因为X与Y线性无关,且Z不能由X与Y线性表示,故X,Y,Z线性无关,它们构成R3中的极大无关组,从而可以表示R3中任意一个向量.

我们是向量x和y在R^3种non-collinear的来源,是向量Z在R^3不在飞机上的X和Y就有可能表达的任何其他途径V在R^的线性组合3个X,Y及Z

http://bishopw.loni.ucla.edu/air5/homogenous.html
see above website
X'= [rotation matrix + translation matrix] X
Y' Y
Z' ...

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http://bishopw.loni.ucla.edu/air5/homogenous.html
see above website
X'= [rotation matrix + translation matrix] X
Y' Y
Z' Z
1 1
X'=X*(cosa*cosb+sina*sinc*sinb)+Y*(sina*cosb-cosa*sinc*sinb)+Z*(cosc*sinb)+ X-shift
Y'=...
Z'=...
1=1

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