Midterm 1

Front 1

Vector space

Back 1

A set of vectors on which two operations are defined, called addition and multiplication by scalars

Front 2

Subspace

Back 2

A subset H of some vector space V such that H has (1) the zero vector of V in H (2) H is closed under vector addition (3) H is closed under multiplication

Front 3

Null space

Back 3

The set NulA of all solutions to the homogenous equation Ax = 0

Front 4

Column space

Back 4

The set ColA of all linear combinations of the columns of A. If A = [v1 ... vn] then Col A = Span{v1... vn}

Front 5

Linear transformation

Back 5

Stuff

Front 6

Basis

Back 6

An indexed set B = {v1, v2, ... vp} in V such that (i) B is a linearly independent set and (ii) the subspace spanned by B coincides with the subspace the basis describes

Front 7

B coordinates of x

Back 7

B = {b1 ... bn}
The weights c1 ... cn in the equation x = c1b1 + ... + cnbn

Front 8

B coordinate vector of x

Back 8

The vector [x]b whose entries are the coordinates of x relative to the basis B

Front 9

Change of coordinates matrix

Back 9

A matrix Pb that transforms B coordinate vectors into C coordinate vectors.
Pbc [x]b = [x]c

Front 10

Isomorphism

Back 10

A one to one linear mapping from one vector space onto another

Front 11

Dimension of a subspace S

Back 11

The number of vectors in a basis for S written as dim S

Front 12

Rank

Back 12

The dimension of the column space of A

Front 13

Row space

Back 13

The set Row A of all linear combinations of the vectors formed from the rows of A; also denoted by Col(A^T)

Front 14

Dimension of a vector space V

Back 14

The number of vectors in a basis for V, written as dim V. The dimension of the zero space is 0.