I'm having a little bit of trouble understanding a passage of my textbook regarding a linear transformation and matrix multiplication, I wonder if you could help me out.
So, I have this equation:
Where F is some 3x3 matrix and x a 3x1 array. For now, these are the important variables. So, my objective is putting F in a specific format called control canonical form (A), which is:
For that, the book shows a Linear Transformation in the variable x:
Which leads to (see first equation):
The equation for A is:
Where T-1 is defined as:
Writing everything in therms of T-1 :
Now, the problem:
I don't understant the right part of the equation. How can I multiply T-1, which is a 3x1 array, with the 3x3 F matrix? Why the book shows a array with every single term of T-1 multiplying F? I apologize if this is some stupid question but linear algebra isn't my strong suit.