







Description 
name 
value 
Name 
value 


R^{2} Euclidean Space >
column vectors 
V1 

V2 










Find Orthonormal Vectors
(set 1) 
U1=V1 

U2 










< U1,U2 > (set 1) 






Normalization Factor 
nu1 

nu2 



Find Normalized Orthonormal
Vectors (set 1) 
e1 

e2 










Decomposition of V into Q & R Matrix 






Q matrix ( orthogonal) 
Q 












R matrix (upper triangular matrix) 
R 












QR= V1V2 
QR 



















Find Orthonormal Vectors
(set 2) 
U1 

U2=V2 










< U1,U2 > (set 2) 






Normalization Factor 
nu3 

nu4 



Find Normalized Orthonormal
Vectors (set 2) 
e1 

e2 










Decomposition of V into Q & R Matrix 






Q matrix (orthogonal) 
Q 












R matrix (lower triangular matrix) 
R 












QR 
QR 

























* If a & b are a pair of vectors
, then vector projections are (a.b)/ (a^{2}) and
(a.b)/ (b^{2})
* For theory, click
here.
* For QR decomposition, click
here. 







