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I am going over these slides and I am very confused on a couple parts. First of all on the first slide, I don't understand why a linear function has the form ##f(x) = c^Tx##. How is that equal to ##c_{1}x_{1} + c_{2}x_{2} + \dots + c_{n}x_{n}##. Wouldn't this depend on how you define ##c## to begin with? What if you just defined ##c## to have the proper matrix deimension to multiply with ##x##?

On the second slide, I am particularly troubled by this sentence ''There is no dependence in the ##c_{\perp}## direction. The function value is constant along these lines.''

I don't understand how the function value is constant. This is probably because I must not know what the function value us. Clearly along any of the given lines, the ##c_{\perp}## is increasing. What do they mean by the function value?

Also, that leads to not understanding the green box on the second slide,

''For ##m##-dimensions, there is a ##(m-1)## dimensional plane, perpendicular to ##c##, and ##c^Tx## has no dependence in those directions''.

What does this mean?

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# Minimizing with constraints and linear function

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