VECTOR SPACES
... • A vector space is called finite dimensional if there is a finite linearly independent set which spans V . Such a set is called a basis for V . The number of vectors in a basis is called the dimension of V . If {v1 , v2 , . . . , vn } is a basis for V then any x in V can be written uniquely in the ...
... • A vector space is called finite dimensional if there is a finite linearly independent set which spans V . Such a set is called a basis for V . The number of vectors in a basis is called the dimension of V . If {v1 , v2 , . . . , vn } is a basis for V then any x in V can be written uniquely in the ...
Chapter 3. Vector - People Server at UNCW
... • The vector components of the vector depend on the orientation of the axes used as a reference. • A scalar is a mathematical quantity whose value does not depend on the orientation of a coordinate system. The magnitude of a vector is a true scalar since it does not change when the coordinate axis i ...
... • The vector components of the vector depend on the orientation of the axes used as a reference. • A scalar is a mathematical quantity whose value does not depend on the orientation of a coordinate system. The magnitude of a vector is a true scalar since it does not change when the coordinate axis i ...
Lecture 14: SVD, Power method, and Planted Graph
... where αmax is the largest coefficient in magnitude. Furthermore, since x was a random unit vector (and recalling that its projection α1 on the fixed vector e1 is normally distributed), the probability is at least 0.99 that α1 > 1/(10n). Thus setting t = O(log n |λ1 | /γ) the components for i ≥ 2 bec ...
... where αmax is the largest coefficient in magnitude. Furthermore, since x was a random unit vector (and recalling that its projection α1 on the fixed vector e1 is normally distributed), the probability is at least 0.99 that α1 > 1/(10n). Thus setting t = O(log n |λ1 | /γ) the components for i ≥ 2 bec ...
