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Non-Negative Vs Positive Semi Definite

Definition of positive definite operator in infinite dimensional spaceImplying a positive definite operatorOperator norm of symmetric Matrix in Hilbert Space with Hermitian Inner ProductHow to prove that $A$ is positive semi-definite if all principal minors are non-negative?Not every positive operator is positive-definite operatorThe composition of a dissipative operator and a positive opeartor is dissipative?Looking for a NON-Symmetric Diagonal Linear Operator!!Commuting matrix with a non-negative matrixRelation between eigenvalues of $0$ in symmetric, non-negative definite operator and its square rootAre Covariance Operators based on square integrable stochastic Processes semi-positive definite?

0

1

$begingroup$

A matrix is PSD if $$langle Ax, xrangle ge 0, forall x in H$$

Where, H is a hilbert space and A is a mapping $H rightarrow H$. Is it the same as being Non-negative? I couldn't seem to find a specific definition for a non-negative operator.

matrices operator-theory hilbert-spaces positive-semidefinite nonnegative-matrices

share|cite|improve this question

edited Mar 14 at 16:49

Hasan Iqbal

asked Mar 13 at 19:02

Hasan IqbalHasan Iqbal

1337

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Non-negative does not make much sense when talking about matrices. When saying non-negative , one is usually talking about real numbers, or integers
  $endgroup$
  – Pink Panther
  Mar 13 at 19:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I would say they are analogous, but the notion of non-negativity for a matrix doesn´t make much sense
  $endgroup$
  – Fede Poncio
  Mar 13 at 19:06
  

  
  
  
  

add a comment | 

0

1

$begingroup$

A matrix is PSD if $$langle Ax, xrangle ge 0, forall x in H$$

Where, H is a hilbert space and A is a mapping $H rightarrow H$. Is it the same as being Non-negative? I couldn't seem to find a specific definition for a non-negative operator.

matrices operator-theory hilbert-spaces positive-semidefinite nonnegative-matrices

share|cite|improve this question

edited Mar 14 at 16:49

Hasan Iqbal

asked Mar 13 at 19:02

Hasan IqbalHasan Iqbal

1337

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Non-negative does not make much sense when talking about matrices. When saying non-negative , one is usually talking about real numbers, or integers
  $endgroup$
  – Pink Panther
  Mar 13 at 19:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I would say they are analogous, but the notion of non-negativity for a matrix doesn´t make much sense
  $endgroup$
  – Fede Poncio
  Mar 13 at 19:06
  

  
  
  
  

add a comment | 

$begingroup$

A matrix is PSD if $$langle Ax, xrangle ge 0, forall x in H$$

Where, H is a hilbert space and A is a mapping $H rightarrow H$. Is it the same as being Non-negative? I couldn't seem to find a specific definition for a non-negative operator.

matrices operator-theory hilbert-spaces positive-semidefinite nonnegative-matrices

share|cite|improve this question

edited Mar 14 at 16:49

Hasan Iqbal

asked Mar 13 at 19:02

Hasan IqbalHasan Iqbal

1337

$endgroup$

share|cite|improve this question

edited Mar 14 at 16:49

Hasan Iqbal

asked Mar 13 at 19:02

Hasan IqbalHasan Iqbal

1337

share|cite|improve this question

edited Mar 14 at 16:49

Hasan Iqbal

asked Mar 13 at 19:02

Hasan IqbalHasan Iqbal

1337

asked Mar 13 at 19:02

Hasan IqbalHasan Iqbal

1337

asked Mar 13 at 19:02

Hasan IqbalHasan Iqbal

1337