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Chapter 4: Vector and Matrix Calculus

https://doi.org/10.1142/9789813275386_0004Cited by:0 (Source: Crossref)

Abstract:

Let 𝔽 be a field, for example the set of real numbers ℝ or the set of complex numbers ℂ. Let m, n ≥ 1 be two integers. An array A of numbers in 𝔽

$(\begin{matrix} a_{11} & a_{12} & a_{13} & \dots & a_{1 n} \\ a_{21} & a_{22} & a_{23} & \dots & a_{2 n} \\ ⋮ & ⋮ & ⋮ & ⋱ & ⋮ \\ a_{m 1} & a_{m 2} & a_{m 3} & \dots & a_{m n} \end{matrix}) = (a_{i j})$

is called an m × n matrix with entry a_ij in the ith row and jth column. A row vector is a 1 × n matrix. A column vector is an n × 1 matrix. If a_ij = 0 for all i, j, then A is called a zero matrix. I_n denotes the n × n identity matrix with the diagonal elements equal to 1 and 0 otherwise…

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Chapter 4: Vector and Matrix Calculus

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