Exam 2 Definitions

Definitions:
Linear Combinations - Any vector can be written as a combination of other vectors
Linear Independence - when two vectors are not scalar multiples
Matrix Inverses - found by row reducing a square matrix $A$ like so $A|I$
Rank - The number of pivots in a row reduced matrix
Subspace - Formed by a span of vectors within another space
Basis - A set of vectors that forms a subspace
Dimension - The number of vectors in the span of an eigenspace
Linear Transformation - Moves a vector using matrix multiplication
Eigenvalues/Eigenvectors - An eigenvalue is a value such that $A$v = $\lambda$v which keeps the same direction after a linear transformation.v is the eigenvector.
Determinants - a number that indicates how a matrix will behave when transformed
Similarity - If A and B are square matrices, and there is some invertible matrix $P$ such that $B=P^{-1}AP$, then $A$ is similar to $B$
Diagonalization - Some matrix A is diagonalizable if it is similar to a diagonal matrix D.