Linear Final

Span

A set of all possible linear combination in a vector

Linear Combination

Created when multiplying each vector by a scalar and adding them togetherto form a new vector.

Linearly Independent

No vectors in the set can be written as a linear combination of others

Linear Transformation

A function from R^n to R^m that satisifies additive and homogenous propertiees

Collumns Space

The set of all possible linear combinations of the column vectors of a matrix

Nullspace

The set of all solutions to the equation Ax=0, subspace of R^m

Transpose

When switching the rows to columns

Inverse

A and B are called this if AB=I and BA=!

Dimensions

The number of vectors in a basis for V

Rank

Number of linearly independent columns

Nullity

Number of free variables

Determinant

A scalar value from a square matrix that determines invertibility

Eigenvalue

A scalar lambda that satisfies the equation Av=lambda*v

Eigenvector

A vector that satisfies x=/= 0, and the equation Ax=lambda*x

Eigenspace

The set of all eigenvectors to the corresponding eigenvalue

Diagonalizable

If we find an inverse matrix P and a diagonal matrix D, the matrix is…

Orthogonal

If all vectors in the set are perpendicular