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A professor is keep using the following kind of matrix. The problem is that I have never seen a matrix separated with these lines inside it. What does that kind of matrix mean (not the contents but the structure)?

enter image description here

This kind of matrix was used for rotational transformations. The 3x3 matrix is a rotation matrix (the contents in the image are picked just to fill the matrix they are not the ones used by the professor). The other contents I don't know what they were used for. That is one other reason I want to know what this matrix is as to find out more about the other contents.

Adam
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    Can you provide somewhat more context? Those partitions lines can have different meanings depending on the context, but generally you can say that they were put there to emphasize a certain structure of the matrix. – flawr Oct 06 '14 at 19:34
  • Ok I will edit my post. – Adam Oct 06 '14 at 19:35

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The matrix is structured into blocks. The zeroes in non-diagonal blocks are related to some stability property.

Consider a matrix of the form $$ A = \begin{pmatrix} a & b & 0 & 0 \\ c & d & 0 & 0 \\ 0 & 0 & e & f \\ 0 & 0 & g & h \end{pmatrix} $$ and assume it is associated to some linear map $\varphi : \mathbb{R}^4 \to \mathbb{R}^4$ with respect to the canonical basis $(e_1, e_2, e_3, e_4)$.

The lower-left block of zeroes means that $\varphi(e_1)$ and $\varphi(e_2)$ belong to the vector susbspace of $\mathbb{R}^4$ spanned by $e_1$ and $e_2$. Thus that subspace is stable under $\varphi$.

Likewise the subspace spanned by $e_3$ and $e_4$ is stable under $\varphi$ as the upper-right block of zeroes suggests.

mandourin
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