In this book the set of integers is denoted by \(\mathbb{Z}\); the nonnegative integers by \(\mathbb{Z}_{+}\); the real rationals by \(\mathbb{Q}\) and the natural numbers 1, 2, …by \(\mathbb{N}\). As usual, \(\mathbb{R}\) and \(\mathbb{C}\) denote the real line and the complex plane, respectively, but also the real and complex number fields. The symbol \(\mathbb{R}_{+} \) means the half-line \([0,\infty )\). If \(z\in\mathbb{C}\) then \(z=\frak{R}(z)+ \frak{J}(z)\sqrt{-1} \) where \(\frak{R}(z)\) and \(\frak{J}(z)\) are real. Since both fields \(\mathbb{R}\) and \(\mathbb{C}\) are needed in definitions, let the symbol \(\mathbb{F}\) indicate either field. \(\mathbb{F}^n\) will denote the n-dimensional linear space of column vectors \(x={\rm col}(x_1,\ldots,x_n)\) whose components are \(x_i\in\mathbb{F}\). Linear and rational symbolic calculations use the field of real rationals \(\mathbb{Q}\) or an algebraic extension of \(\mathbb{Q}\) such as the complex rationals \(\mathbb{Q}(\sqrt{-1})\).
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Elliott, D.L. (2009). Matrix Algebra. In: Bilinear Control Systems. Applied Mathematical Sciences, vol 169. Springer, Dordrecht. https://doi.org/10.1023/b101451_9
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DOI: https://doi.org/10.1023/b101451_9
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