represent a matrix with constants

Hi all can someone tell me how to represent these matrices in matlab I just want to represent them so I can find the inverse and other related matrices but I dont have an actual angle

[John D'Errico]

What have you tried? If nothing, why not? Do you have the symbolic toolbox?

Lacking that, I'll point out they are rotation matrices. What useful property does the transpose of such a rotation matrix have? Do you really need to compute the inverse? (Hint: read that sentence about the transpose again.)

Answer 1

[David Ding]

Hi,

If you really need to store these matrices in MATLAB without an angle in mind, you may wish to use functions where the input argument is the angle and the output is the matrix.

For example, say you need the matrix

[sin \theta, cos \theta; -cos \theta, sin \theta]

You can do something like this:

function matrixOut = genMatrix (angle)
matrixOut = [sin(angle), cos(angle); -cos(angle), sin(angle)];
end

If you wish to store the matrix in the base workspace where the angle is just a symbol or variable in your workflow, then you may use the Symbolic Math Toolbox to help you:

Example:

>> syms x
>> myMatrix = [sin(x), cos(x); -cos(x), sin(x)]

myMatrix =

[  sin(x), cos(x)]
[ -cos(x), sin(x)]

>> B = inv(myMatrix) % calculate the inverse of the matrix "myMatrix"

B =

[ sin(x)/(cos(x)^2 + sin(x)^2), -cos(x)/(cos(x)^2 + sin(x)^2)]
[ cos(x)/(cos(x)^2 + sin(x)^2),  sin(x)/(cos(x)^2 + sin(x)^2)]