How to show that every symmetric nonsingular complex matrix can be written as $A=P^ T P$ form
I know that if we have a positive definite matrix then we can show that A=$P^T P$
But here I had given to prove for a complex matrix which needs to be hermitian.
It is not duplicate AS My question is for symmetric complex matrix Not Hermitian
Please help me
I'm stuck here, any hint will be appreciated
linear-algebra bilinear-form
asked Nov 25 at 14:59
MathLover
45710
add a comment |
I know that if we have a positive definite matrix then we can show that A=$P^T P$
But here I had given to prove for a complex matrix which needs to be hermitian.
It is not duplicate AS My question is for symmetric complex matrix Not Hermitian
Please help me
I'm stuck here, any hint will be appreciated
linear-algebra bilinear-form
asked Nov 25 at 14:59
MathLover
45710
1
Sir I have symmetric complex matrix I read it is for real hermitian
– MathLover
Nov 25 at 15:10
1
Look for Takagi's factorization: write $A=U^TDU$ and split $D=D^{1/2}D^{1/2}$.
– A.Γ.
Nov 25 at 15:47
1
See also Wiki
– A.Γ.
Nov 25 at 18:28
add a comment |
I know that if we have a positive definite matrix then we can show that A=$P^T P$
But here I had given to prove for a complex matrix which needs to be hermitian.
It is not duplicate AS My question is for symmetric complex matrix Not Hermitian
Please help me
I'm stuck here, any hint will be appreciated
linear-algebra bilinear-form
asked Nov 25 at 14:59
MathLover
45710
I know that if we have a positive definite matrix then we can show that A=$P^T P$
But here I had given to prove for a complex matrix which needs to be hermitian.
It is not duplicate AS My question is for symmetric complex matrix Not Hermitian
Please help me
I'm stuck here, any hint will be appreciated
linear-algebra bilinear-form
linear-algebra bilinear-form
asked Nov 25 at 14:59
MathLover
45710
asked Nov 25 at 14:59
MathLover
45710
edited Nov 25 at 15:17
asked Nov 25 at 14:59
MathLover
45710
asked Nov 25 at 14:59
MathLover
45710
asked Nov 25 at 14:59
MathLover
45710
45710
1
Sir I have symmetric complex matrix I read it is for real hermitian
– MathLover
Nov 25 at 15:10
1
Look for Takagi's factorization: write $A=U^TDU$ and split $D=D^{1/2}D^{1/2}$.
– A.Γ.
Nov 25 at 15:47
1
See also Wiki
– A.Γ.
Nov 25 at 18:28
add a comment |
1
Sir I have symmetric complex matrix I read it is for real hermitian
– MathLover
Nov 25 at 15:10
1
Look for Takagi's factorization: write $A=U^TDU$ and split $D=D^{1/2}D^{1/2}$.
– A.Γ.
Nov 25 at 15:47
1
See also Wiki
– A.Γ.
Nov 25 at 18:28
1
1
Sir I have symmetric complex matrix I read it is for real hermitian
– MathLover
Nov 25 at 15:10
Sir I have symmetric complex matrix I read it is for real hermitian
– MathLover
Nov 25 at 15:10
1
1
Look for Takagi's factorization: write $A=U^TDU$ and split $D=D^{1/2}D^{1/2}$.
– A.Γ.
Nov 25 at 15:47
Look for Takagi's factorization: write $A=U^TDU$ and split $D=D^{1/2}D^{1/2}$.
– A.Γ.
Nov 25 at 15:47
1
1
See also Wiki
– A.Γ.
Nov 25 at 18:28
See also Wiki
– A.Γ.
Nov 25 at 18:28
add a comment |
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1
Sir I have symmetric complex matrix I read it is for real hermitian
– MathLover
Nov 25 at 15:10
1
Look for Takagi's factorization: write $A=U^TDU$ and split $D=D^{1/2}D^{1/2}$.
– A.Γ.
Nov 25 at 15:47
1
See also Wiki
– A.Γ.
Nov 25 at 18:28