Statistical Signal Processing in Engineering

1Manipulations on Matrixes

Even if matrix algebra requires some basic analytic tools in order to handle it with confidence, the benefits are huge compared to the price paid. This chapter, and those that follow, aim to make a review of these basic operations.

1.1 Matrix Properties

ℝⁿ and ℂⁿ represent the ensemble of all the ordered tuples of n real/complex numbers (x₁, x₂, …, x_n). Each of these tuples can be seen as the coordinate of a point in n ‐dimensional (or 2n ‐dimensional) space. Normally these tuples of n numbers are ordered in column vectors . The notation indicates that x is an ordered tuple (column vector) of n real numbers that define a vector in ℝⁿ; similarly for . A matrix is obtained by juxtaposing a set of column vectors (tuples): obtaining (or if complex‐valued). The (i, j) entry of X (i and j indicate the row and column index, respectively) is indicated by , depending ...