Usbrth

What's the difference between (size_t)-1 and ~0?

How should I respond to a player wanting to catch a sword between their hands?

Strange behaviour of Check

What did Darwin mean by 'squib' here?

Fishing simulator

Interesting examples of non-locally compact topological groups

Can smartphones with the same camera sensor have different image quality?

Working around an AWS network ACL rule limit

How can I make names more distinctive without making them longer?

If A makes B more likely then B makes A more likely"

Array/tabular for long multiplication

The following signatures were invalid: EXPKEYSIG 1397BC53640DB551

Unable to start mainnet node docker container

Am I ethically obligated to go into work on an off day if the reason is sudden?

When is phishing education going too far?

How to add zeros to reach same number of decimal places in tables?

Estimated State payment too big --> money back; + 2018 Tax Reform

Passing functions in C++

What is the electric potential inside a point charge?

What kind of display is this?

Determine whether f is a function, an injection, a surjection

Limit for e and 1/e

Using "nakedly" instead of "with nothing on"

Direct Experience of Meditation

Skew symmetric matrix of vector follow up - How to obtain skew matrix for N-dimensional vector

0

$begingroup$

I am trying to understand usage of skew matrices:

1) It is my understanding from an earlier question in this forum that for vectors A and B, that A cross B is the same as the "skew symmetric matrix" of A times B. Is this correct?

2) If the above is correct, I did a simple example in matlab where A = [1 0 0] and B = [0 1 0]. The obvious cross product is C = [0 0 1];
The skew multiplication is Sij = AiBj - AjBi which results in [0 1 0;-1 0 0; 0 0 0], but the skew of C, or AxB, is [0 -1 0; 1 0 0; 0 0 0]. Looks like the two results are negated or transposed. So I am not sure how this is equivalent, but maybe I just don't understand the application. Any explanation is appreciated.

3) If skew multiplication is a generalization to N dimensional vectors of the cross product when N = 3, then is there an example of finding an orthogonal vector to two vectors in 4-D? All the examples I can find show the equivalent skew matrix for a 3-D vector and how that multiplied with another 3-D vector results in the cross product vector, but I see no reference for getting the skew mapping for N dimensional vectors so that you can multiply that with another N-dimensional vector to obtain an orthogonal N-D vector.

Thanks in advance

linear-algebra matrices lie-algebras

share|cite|improve this question

asked Apr 8 at 19:36

lee84lee84

1

New contributor

lee84 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to Math.SE! Please use MathJax to format your posts.
  $endgroup$
  – csch2
  Apr 8 at 20:02
  

  
  
  
  

add a comment | 

0

$begingroup$

I am trying to understand usage of skew matrices:

1) It is my understanding from an earlier question in this forum that for vectors A and B, that A cross B is the same as the "skew symmetric matrix" of A times B. Is this correct?

2) If the above is correct, I did a simple example in matlab where A = [1 0 0] and B = [0 1 0]. The obvious cross product is C = [0 0 1];
The skew multiplication is Sij = AiBj - AjBi which results in [0 1 0;-1 0 0; 0 0 0], but the skew of C, or AxB, is [0 -1 0; 1 0 0; 0 0 0]. Looks like the two results are negated or transposed. So I am not sure how this is equivalent, but maybe I just don't understand the application. Any explanation is appreciated.

3) If skew multiplication is a generalization to N dimensional vectors of the cross product when N = 3, then is there an example of finding an orthogonal vector to two vectors in 4-D? All the examples I can find show the equivalent skew matrix for a 3-D vector and how that multiplied with another 3-D vector results in the cross product vector, but I see no reference for getting the skew mapping for N dimensional vectors so that you can multiply that with another N-dimensional vector to obtain an orthogonal N-D vector.

Thanks in advance

linear-algebra matrices lie-algebras

share|cite|improve this question

asked Apr 8 at 19:36

lee84lee84

1

New contributor

lee84 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to Math.SE! Please use MathJax to format your posts.
  $endgroup$
  – csch2
  Apr 8 at 20:02
  

  
  
  
  

add a comment | 

$begingroup$

I am trying to understand usage of skew matrices:

1) It is my understanding from an earlier question in this forum that for vectors A and B, that A cross B is the same as the "skew symmetric matrix" of A times B. Is this correct?

2) If the above is correct, I did a simple example in matlab where A = [1 0 0] and B = [0 1 0]. The obvious cross product is C = [0 0 1];
The skew multiplication is Sij = AiBj - AjBi which results in [0 1 0;-1 0 0; 0 0 0], but the skew of C, or AxB, is [0 -1 0; 1 0 0; 0 0 0]. Looks like the two results are negated or transposed. So I am not sure how this is equivalent, but maybe I just don't understand the application. Any explanation is appreciated.

3) If skew multiplication is a generalization to N dimensional vectors of the cross product when N = 3, then is there an example of finding an orthogonal vector to two vectors in 4-D? All the examples I can find show the equivalent skew matrix for a 3-D vector and how that multiplied with another 3-D vector results in the cross product vector, but I see no reference for getting the skew mapping for N dimensional vectors so that you can multiply that with another N-dimensional vector to obtain an orthogonal N-D vector.

Thanks in advance

linear-algebra matrices lie-algebras

share|cite|improve this question

asked Apr 8 at 19:36

lee84lee84

1

New contributor

lee84 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

asked Apr 8 at 19:36

lee84lee84

1

New contributor

lee84 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

asked Apr 8 at 19:36

lee84lee84

1

New contributor

lee84 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Apr 8 at 19:36

lee84lee84

1

New contributor

lee84 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Apr 8 at 19:36

lee84lee84

1