# Matrix equation notation

I have been reading through a paper and saw a notation that i did not know about. It says that we have to solve the matrix equation $\Delta \mathrm{h}'=\mathrm{Lh}'$. That it clear to me, but what does the following mean: Image of equation.

I was not able to find any information on what that means. Can anybody tell man or atleast give me some keywords to help me.

• Depends on the context. Need more information, e.g., which paper? Commented Oct 26, 2016 at 20:31

I will start with the left-most matrix, as I think this is what you will be struggling the most. This defines a $(k-b+1)\times k$ matrix. It means that the first $k$ rows and $k$ columns of the matrix consist of the $k\times k$ matrix $L$. Then, below this, we have an identity matrix in the bottom right corner, of size $(k-b+1)\times (k-b+1)$ Then, the gaps on the left hand side are filled by zeros.

This may be better explained by example. Let's take $k=5$ and $b=3$ and let $$L=\begin{pmatrix} 1&3&2&1&8\\ 9&7&0&1&3\\ 2&3&1&1&4\\ 7&0&1&3&10\\ 8&1&9&3&2 \end{pmatrix}.$$

Then the matrix described by your picture is

$$\begin{pmatrix} 1&3&2&1&8\\ 9&7&0&1&3\\ 2&3&1&1&4\\ 7&0&1&3&10\\ 8&1&9&3&2\\ 0&0&1&0&0\\ 0&0&0&1&0\\ 0&0&0&0&1 \end{pmatrix}$$

If, instead, we let $b=2$ then we would obtain the following matrix.

$$\begin{pmatrix} 1&3&2&1&8\\ 9&7&0&1&3\\ 2&3&1&1&4\\ 7&0&1&3&10\\ 8&1&9&3&2\\ 0&1&0&0&0\\ 0&0&1&0&0\\ 0&0&0&1&0\\ 0&0&0&0&1 \end{pmatrix}$$

Then, according to your picture, we are multiplying this matrix by another matrix $h'$ and obtaining another matrix consisting of $(\Delta h)'$ at the top and 0's underneath (to make up the required dimension of the matrix).