Matrices

[Harry_the_cat]

Usually as a column.

 

[Steven G]

Identity matrices are always square matrices?

When you multiply the ith row of the ID matrix with another matrix you get back the ith row of the other matrix.

 

[Agent Smith]

When you multiply the ith row of the ID matrix with another matrix you get back the ith row of the other matrix.

Correct! Gracias.

 

[Agent Smith]

Usually as a column.

However, that's only convention, right? Or is there a good reason to use column vectors rather than row vectors?

 

[Harry_the_cat]

The transformation matrix is placed on the left. So for the multiplication to be possible, the vector must be written as a column.

 

[Dr.Peterson]

However, that's only convention, right? Or is there a good reason to use column vectors rather than row vectors?

The transformation matrix is placed on the left. So for the multiplication to be possible, the vector must be written as a column.

I've seen some contexts in which row vectors were used, and matrix operators were on the right. That is mentioned here:

Row and column vectors - Wikipedia

en.wikipedia.org

So, yes, it is a convention, and we can go either way. Either way, something is different from what students initially expect!

 

[Agent Smith]

Is there a website where I can apply a 2 x 2 transformation matrix to a picture?