Finite-Dimensional Hilbert Space and The Linear Inverse Problem
نویسنده
چکیده
Linear Vector Space. A Vector Space, X , is a collection of vectors, x ∈ X , over a field, F , of scalars. Any two vectors x, y ∈ X can be added to form x+y ∈ X where the operation “+” of vector addition is associative and commutative. The vector space X must contain an additive identity (the zero vector 0) and, for every vector x, an additive inverse −x. The required properties of vector addition are given on page 160 of the textbook by Meyer. The properties of scalar multiplication, αx = α · x, of a vector x ∈ X by a scalar α ∈ F are also given on page 160 of Meyer. The scalars used in this course are either the field of real numbers, F = R, or the field of complex numbers, F = C. In this course, we consider only finite dimensional vector spaces dimX = n < ∞.3 Any vector x in an n–dimensional vector space can be represented as an n–tuple (n × 1 column
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