A^c Notation in Matrix: Exploring the Unknown

[utkarshakash]

Homework Statement

What is meant by $A^c$ notation in matrix, where A is any arbitrary matrix?

The Attempt at a Solution

I've searched all over the internet and reference books that I have but none of them gives information about this thing. Please help me.

 

[Mark44]

Homework Statement

What is meant by $A^c$ notation in matrix, where A is any arbitrary matrix?

The Attempt at a Solution

I've searched all over the internet and reference books that I have but none of them gives information about this thing. Please help me.

Could you give us some context for this notation, such as where you saw it and some of the explanatory text? Are the entries in the matrix complex? If so, A^C might mean the conjugate of A. I have never seen this notation before.

 

[utkarshakash]

Could you give us some context for this notation, such as where you saw it and some of the explanatory text? Are the entries in the matrix complex? If so, A^C might mean the conjugate of A. I have never seen this notation before.

At first I also suspected that it should be conjugate. But the matrix in the original question was not complex. I had to select an option from 4 given options. If I assume the notation to be conjugate then there would be three correct options which is not possible. That's why, I'm ruling out the possibility of conjugate notation.

 

[Mark44]

What are the four options? That might help us understand what the notation is supposed to mean. Also, check your textbook to see if they have defined this notation.

 

[Ross1]

It is the compliment set of A, everything not in A.

 

[haruspex]

It is the compliment set of A, everything not in A.

You mean 'complement', but A is given to be a matrix, not a set.

 

[utkarshakash]

What are the four options? That might help us understand what the notation is supposed to mean. Also, check your textbook to see if they have defined this notation.

Here's the original question

$A = \left[ \begin{array}{cc} \cos \theta & \sin \theta \\ - \sin \theta & \cos \theta \end{array} \right] \\ B = \left[ \begin{array}{cc} \sin \theta & \cos \theta \\ - \cos \theta & \sin \theta \end{array} \right]$

Four options are

$A = B^{-1} \\ A^c = B^{-1} \\ A^c = (B^c)^{-1} \\ A^{-1} = B^c$

Now If I suppose A^c to be conjugate of A then there is no difference between first 3 options as A^c = A, because the matrix does not contain complex variables.

 

[haruspex]

Here's the original question

$A = \left[ \begin{array}{cc} \cos \theta & \sin \theta \\ - \sin \theta & \cos \theta \end{array} \right] \\ B = \left[ \begin{array}{cc} \sin \theta & \cos \theta \\ - \cos \theta & \sin \theta \end{array} \right]$

Four options are

$A = B^{-1} \\ A^c = B^{-1} \\ A^c = (B^c)^{-1} \\ A^{-1} = B^c$

Now If I suppose A^c to be conjugate of A then there is no difference between first 3 options as A^c = A, because the matrix does not contain complex variables.

So compute AB. can you figure out what the resulting matrix does to the plane?