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$\ppt$ & Probabilistic Polynomial Time \\
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$\epsilon$ & empty word \\
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$\mathbf A$ & bold uppercase letters represent matrices\\
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$\mathbf b$ & bold lowercase letters represent vectors\\
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$\mathbf b$ & bold lowercase letters represent column vectors\\
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$\widetilde{\mathbf A}$ & Gram-Schmidt orthogonalization of matrix $\mathbf A$\\
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$\mathbf{A}^T_{}, \mathbf{u}^T_{}$ & the transpose of a matrix or a vector respectively\\
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[1ex] \multicolumn{2}{l}{\scbf{Usual sets}} \\
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$\QQ$ & the set of rational numbers \\
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$\RR$ & the set of real numbers \\
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