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1

$begingroup$

The characteristic equation of matrix A is
$$lambda ^3 - I_1lambda^2 + I_2lambda-I_3 = 0 $$

For orthogonal matrix
$$I_3 = det(A) = pm1$$
$$I_1 = tr(A)$$

Taking examples of orthogonal matrices, it looks like $I_1 = I_2$. Is this true always for an orthogonal matrix? Is there some proof?

linear-algebra matrices trace orthogonal-matrices

share|cite|improve this question

edited Mar 12 at 21:31

Yanior Weg

2,51911246

asked Mar 12 at 16:11

JamesJames

62

New contributor

James is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax.
  $endgroup$
  – dantopa
  Mar 12 at 16:51
  

  
  
  
  

add a comment | 

1

$begingroup$

The characteristic equation of matrix A is
$$lambda ^3 - I_1lambda^2 + I_2lambda-I_3 = 0 $$

For orthogonal matrix
$$I_3 = det(A) = pm1$$
$$I_1 = tr(A)$$

Taking examples of orthogonal matrices, it looks like $I_1 = I_2$. Is this true always for an orthogonal matrix? Is there some proof?

linear-algebra matrices trace orthogonal-matrices

share|cite|improve this question

edited Mar 12 at 21:31

Yanior Weg

2,51911246

asked Mar 12 at 16:11

JamesJames

62

New contributor

James is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please use MathJax.
  $endgroup$
  – dantopa
  Mar 12 at 16:51
  

  
  
  
  

add a comment | 

$begingroup$

The characteristic equation of matrix A is
$$lambda ^3 - I_1lambda^2 + I_2lambda-I_3 = 0 $$

For orthogonal matrix
$$I_3 = det(A) = pm1$$
$$I_1 = tr(A)$$

Taking examples of orthogonal matrices, it looks like $I_1 = I_2$. Is this true always for an orthogonal matrix? Is there some proof?

linear-algebra matrices trace orthogonal-matrices

share|cite|improve this question

edited Mar 12 at 21:31

Yanior Weg

2,51911246

asked Mar 12 at 16:11

JamesJames

62

New contributor

James is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited Mar 12 at 21:31

Yanior Weg

2,51911246

asked Mar 12 at 16:11

JamesJames

62

New contributor

James is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited Mar 12 at 21:31

Yanior Weg

2,51911246

asked Mar 12 at 16:11

JamesJames

62

New contributor

James is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited Mar 12 at 21:31

Yanior Weg

2,51911246

edited Mar 12 at 21:31

Yanior Weg

2,51911246

asked Mar 12 at 16:11

JamesJames

62

New contributor

James is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 12 at 16:11

JamesJames

62