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3

$begingroup$

Given a 2x2 matrix,
$$beginbmatrix1&-1\-1&frac12endbmatrix$$
What geometric effect does it have?

So a way I did to solve this was to simply apply it to a unit square that I drew on a graph paper and see what the new image looks like.

Picture of transformation:

To me it looks like a reflection, followed by shearing. But this is where I get lost...

I understand that you can first do a rotation, followed by a shear, and the product of these two transformation matrix will give you a matrix that does the two transformation.

I guess what I'm specifically asking is, is there a way to derive how I can get to this $A$ matrix?

Or am I wrong to think of it that way.

matrices transformation

share|cite|improve this question

edited Mar 14 at 5:13

Parcly Taxel

44.7k1376109

asked Mar 14 at 4:52

NattymathsNattymaths

161

New contributor

Nattymaths is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What's its eigenvalues?
  $endgroup$
  – Lord Shark the Unknown
  Mar 14 at 5:18
  

  
  
  
  

add a comment | 

3

$begingroup$

Given a 2x2 matrix,
$$beginbmatrix1&-1\-1&frac12endbmatrix$$
What geometric effect does it have?

So a way I did to solve this was to simply apply it to a unit square that I drew on a graph paper and see what the new image looks like.

Picture of transformation:

To me it looks like a reflection, followed by shearing. But this is where I get lost...

I understand that you can first do a rotation, followed by a shear, and the product of these two transformation matrix will give you a matrix that does the two transformation.

I guess what I'm specifically asking is, is there a way to derive how I can get to this $A$ matrix?

Or am I wrong to think of it that way.

matrices transformation

share|cite|improve this question

edited Mar 14 at 5:13

Parcly Taxel

44.7k1376109

asked Mar 14 at 4:52

NattymathsNattymaths

161

New contributor

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

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What's its eigenvalues?
  $endgroup$
  – Lord Shark the Unknown
  Mar 14 at 5:18
  

  
  
  
  

add a comment | 

$begingroup$

Given a 2x2 matrix,
$$beginbmatrix1&-1\-1&frac12endbmatrix$$
What geometric effect does it have?

So a way I did to solve this was to simply apply it to a unit square that I drew on a graph paper and see what the new image looks like.

Picture of transformation:

To me it looks like a reflection, followed by shearing. But this is where I get lost...

I understand that you can first do a rotation, followed by a shear, and the product of these two transformation matrix will give you a matrix that does the two transformation.

I guess what I'm specifically asking is, is there a way to derive how I can get to this $A$ matrix?

Or am I wrong to think of it that way.

matrices transformation

share|cite|improve this question

edited Mar 14 at 5:13

Parcly Taxel

44.7k1376109

asked Mar 14 at 4:52

NattymathsNattymaths

161

New contributor

Nattymaths 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 14 at 5:13

Parcly Taxel

44.7k1376109

asked Mar 14 at 4:52

NattymathsNattymaths

161

New contributor

Nattymaths 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 14 at 5:13

Parcly Taxel

44.7k1376109

asked Mar 14 at 4:52

NattymathsNattymaths

161

New contributor

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

edited Mar 14 at 5:13

Parcly Taxel

44.7k1376109

edited Mar 14 at 5:13

Parcly Taxel

44.7k1376109

asked Mar 14 at 4:52

NattymathsNattymaths

161

New contributor

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

asked Mar 14 at 4:52

NattymathsNattymaths

161