Thread: matrix

Nice to see the forum back again. It has been down for weeks hasn't it?

A question says: "Cayley proved in 1946 that, if S is a skew-symmetric matrix, then I+S is non-singular and A=(I-S)(I+S)^-1 is orthogonal. Find A when S=(0 3, -3 0) and show that it is orthogonal."

The second row of S is -3 0. I don't know why I am not able to find A. I will probably manage the final part myself.

$\begin{bamtrix}1 & 0\\
0 & 1
\end{batrix}-
\begin{bmatrix}
0 & 3\\
-3 & 0
\end{bmatrix} =
\begin{bmatrix}
1 & -3
3 & 1
\end{bmatrix}$

So then what is I + S?

Let B=I+S. Then the inverse of B is
$\frac{1}{\text{det}(B)}\begin{matrix}
b_{22} & -b_{21}\\
-b_{12} & b_{11}
\end{bmatrix}$

Is The Matrix,
| 0 3 |
| -3 0 |
And,
| 1 -3|
| 3 1 |

IF these are the two matrices please tell everyone, Please also Define I & S
A series of good videa tutorials on matrices can be found !

Sorry, didnt realise there was a post above the one shown on my screen. I see the question now i am just gonna leave my post as it is for now though. sorry.

The first matrix you give is S. I had been making a mistake by multiplying by the determinant instead of dividing. The expression is straightforward to evaluate. The last part is done using the property AxAtranspose=I.