Summary: Mathematical Vocabulary for Math 320
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1. M 320
Vectors v1, · · · , vk are linearly independent if the only solution to c1v1+· · ·+ckvk = 0
is c1 = · · · = ck = 0.
To span Vectors v1, · · · , vk span a linear subspace L of Rn if every vector in L is a linear com-
bination of the vectors v1, · · · , vk.
Linear subspace If L is a set of vectors in Rn, then L is a linear subspace of Rn if
(i) for any two vectors u L, v L the sum u + v also belongs to L, and
(ii) for any vector v L and any number c, the vector cv also belongs to L.
Solution space e solution space of a set of homogeneous linear equations Ax = 0 is the set whi
consists of all vectors x whi satisfy the equation. is notion is only used for homo-
Basis Vectors v1, ..., vn form a basis for a linear subspace L if they are linearly independent,
and if they span L.
Dimension e dimension of a linear subspace L of Rn is the number of vectors in a basis for L.