Appendix AVectors and Matrices
A.1 Vectors and Norms
A vector is an array of real or complex numbers. We denote vectors by lowercase bold letters and assume a vector to be a column vector. For example, a vector of length n is
The number of elements in a vector is also known as the dimension of the vector. If the elements x1, x2,... , xn are real, then we say that x is a real n-dimensional vector, and we can denote it as . On the other hand, if the elements are complex, then we say that x is a complex n-dimensional vector, and it is denoted as .
Various norms are defined to measure the magnitude of a vector. One such measure is ℓp norm, which is defined as
where n is the dimension of ...