CHAPTER 2

VECTOR SPACES AND MATRICES

2.1 Vector and Matrix

We define a column n-vector to be an array of n numbers, denoted

equation

The number ai is called the ith component of the vector a. Denote by the set of real numbers and by n the set of column n-vectors with real components. We call n an n-dimensional real vector space. We commonly denote elements of n by lowercase bold letters (e.g., x). The components of x n are denoted x1, …, xn.

We define a row n-vector as

equation

The transpose of a given column vector a is a row vector with corresponding elements, denoted a. For example, if

then

Equivalently, ...

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