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Merging two orthonormal bases without Gram-Schmidt

1

$begingroup$

I have two sets of column vectors: $A = a_1,a_2,dotsc,a_m$ and $B = b_1,b_2,dotsc,b_n$. I have orthornormal basis for both of them individiaully. $u_1,dotsc,u_p$ is an othornormal basis for $A$ and $v_1,dotsc,v_p$ is an othornormal basis for $B$.

Is there a way to find an orthonormal basis for $Acup B$ without using Gram -Schmidt orthogonalization on $u_icup v_i$?.

linear-algebra orthonormal

share|cite|improve this question

asked Mar 24 at 16:14

dexter04dexter04

1,6851027

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  There are other algorithms.
  $endgroup$
  – user647486
  Mar 24 at 16:31
  

  
  
  
  

add a comment | 

1

$begingroup$

I have two sets of column vectors: $A = a_1,a_2,dotsc,a_m$ and $B = b_1,b_2,dotsc,b_n$. I have orthornormal basis for both of them individiaully. $u_1,dotsc,u_p$ is an othornormal basis for $A$ and $v_1,dotsc,v_p$ is an othornormal basis for $B$.

Is there a way to find an orthonormal basis for $Acup B$ without using Gram -Schmidt orthogonalization on $u_icup v_i$?.

linear-algebra orthonormal

share|cite|improve this question

asked Mar 24 at 16:14

dexter04dexter04

1,6851027

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  There are other algorithms.
  $endgroup$
  – user647486
  Mar 24 at 16:31
  

  
  
  
  

add a comment | 

$begingroup$

I have two sets of column vectors: $A = a_1,a_2,dotsc,a_m$ and $B = b_1,b_2,dotsc,b_n$. I have orthornormal basis for both of them individiaully. $u_1,dotsc,u_p$ is an othornormal basis for $A$ and $v_1,dotsc,v_p$ is an othornormal basis for $B$.

Is there a way to find an orthonormal basis for $Acup B$ without using Gram -Schmidt orthogonalization on $u_icup v_i$?.

linear-algebra orthonormal

share|cite|improve this question

asked Mar 24 at 16:14

dexter04dexter04

1,6851027

$endgroup$

share|cite|improve this question

asked Mar 24 at 16:14

dexter04dexter04

1,6851027

share|cite|improve this question

asked Mar 24 at 16:14

dexter04dexter04

1,6851027

asked Mar 24 at 16:14

dexter04dexter04

1,6851027

asked Mar 24 at 16:14

dexter04dexter04

1,6851027