• Mathematics

    The Rank of a Matrix with some Association with Machine Learning and Quantum Computing

    Introduction General Definition Some results involving the rank of a matrix Theorem 5.1 (Ivanyos et al., 2018) Lemma 5.2 (Ivanyos et al., 2018) Rank of a matrix in machine learning Low-rank matrix approximation  Apache Spark: a computer framework for matrix computation  Rank of a matrix in quantum information Kraus Operators   Introduction (back to outline) For a matrix \[A=\left[\begin{array}{ccc}0 & -1 & 1\\1 & 2 & -1\\1 & 1 & 3\end{array}\right],\] where each entry is a real number, the columns of $A$ form a linearly independent set of vectors of $\mathbb{R}^{3}$, so the subspace generated by the three columns is of dimension $3$, which is isomorphic to $\mathbb{R}^{3}$. The dimension…