I am fundamentally missing something and would appreciate some clarification. I am reading the book Statistical Image Processing and Multidimensional Modeling on Regularized Least Squares. This text has a problem where I have to find z, a set of unknown elements. z in this case is a column vector of five 2D points.
To compute $\hat{z}$, I use the following equation (provided by the text):
$$\hat{z} = (C^TR^{-1}C+\lambda LL^T)^{-1}C^TR^{-1}\vec{m}$$
where C is the transformation matrix, L is the constraint matrix, $\vec{m}$ is the measurement column vector and R is an Identity matrix.
$$\vec{m} = C\vec{z} + \vec{v} = \begin{bmatrix}z_{1}\\z_{5}\end{bmatrix} +\vec{v}$$
where $\vec{v}$ ~ I and $\vec{m} = \begin{bmatrix}10\\50\end{bmatrix}$
Here's the thing this problem is set on a 2D plane, so z is a vector of 2D (x,y) points. However, the text does not give m, a set of measurements on the 2D plane, in the same type. Instead m is a column vector of [10;50]. This reduces z to a column vector as well.
The question then asks us to plot z. How can I plot z if I have only a column vector?
What am I missing here?
I think you can set the vector $\vec{z}$ in the following form \begin{equation} \vec{z} = \begin{pmatrix} x_1\\ y_1\\ x_2\\ y_2\\ \vdots\\ x_n\\ y_n \end{pmatrix}, \end{equation} or, for example, in the following form \begin{equation} \vec{z}= \begin{pmatrix} x_1\\ x_2\\ \vdots\\ x_n\\ y_1\\ y_2\\ \vdots\\ y_n \end{pmatrix}. \end{equation}