===========
 Exercises
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#. **Fully Connected Network.** Given a grayvalue image $f$ of size
   $N\times N$ and a resulting image $g$ of the same size, calculate
   the dimensions of the weight matrix $W$ as used in the equation $\v
   g = W \v f$ (see Eq. :eq:`eq-conv-matrix-vector`).


#. **Convolution/Correlation as Matrix-Vector Multiplication.**

   a. In Eq. :eq:`eq-Wcorrelation` the matrix corresponding with a
      correlation with a small kernel of a $4\times4$ image is
      shown. Which border mode is implicitly used (either the constant
      value mode (what value?) or wrap mode)?

   b. What does the matrix $W$ looks like for the other border mode?