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The notation $A^T$ stands for the transpose of a matrix. It is not specific to machine learning, but rather standard notation in linear algebra. Other notations are sometimes used, for example $A'$. A related operation is the adjoint $A^*$. The transpose and adjoint are equal for real matrices.

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This may take the form of a quantity which is asserted to decrease continually and vanish when the machine stops. Lambda calculus evaluation is a sequence of beta reduction steps. So for the lambda calculus (with or without types: types don't affect evaluation), you want a quantity (a positive integer) that decreases at each reduction step. Such a quantity ...

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After some research, I think I can answer this question by myself now. Short answer Wikipedia is correct, that is If the $\lambda$-calculus uses call by value reduction strategy, the term $(\lambda x.x)(y y)$ is a normal form. Long answer Standard $\lambda$-calculus does not distinguish reduction strategies. It only gives you some Reduction Rules (e.g. \$\...

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