| | |
Summary: Mathematical Vocabulary for Math 320
is document is not finished: as the class progresses new items will be added, and you should add items
of your own. Che the textbook to see if you can find where these concepts are defined. Write the page
numbers next to the definitions on this sheet.
1. M 320
Linear
independence
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-
geneous equations.
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.
|
