E$7\mathrm{.}8$ Consider the three prototype patterns shown in Figure E$7\mathrm{.}2.$

i$.$ Are these patterns orthogonal? Demonstrate.

ii$.$ Use the Hebb rule to determine the weight matrix for a linear au$-$

toassociator to recognize these patterns.

iii. Draw the network diagram.

Exercises

iv$.$ Find the eigenvalues and eigenvectors of the weight matrix. $($Do not

solve the equation $|W-I|=0.$ Use an analysis of the Hebb

rule.$)$

Figure E$7\mathrm{.}2$ Prototype Patterns for Exercise E$7\mathrm{.}8$