Final Flashcards
Ax=(L)x
L is an eigenvalue and x is an eigenvector
eigenspace associated with the eigenvalue of a matrix A
the null space of (A-(L)I)
a diagonal matrix
square matrix where only non zero entries are along the diagonal
a matrix is diagonalizable iff
the columns of P are n linearly independent eigenvectors of A
if a matrix is diagonalizable
the diagonal entries of D are the eigenvalues of A that correspond to the eigenvectors in P
A is diagonalizable if
the algebraic multiplicity of all eigenvalues of a matrix A are 1
the dot product or inner product
u(transpose)*v or u.v
a vector with length 1
unit vector
two vectors are orthogonal if
u.v=0
the orthogonal component of w
wperp=span()
if w is a subspace of R^n
wperp is a subspace of R^n
an orthogonal set
a set of vectors where each distinct pair is orthogonal
orthogonal matrix
a matrix whose columns form an orthonormal set (AKA U)
U is an orthogonal matrix if and only iff
U(T)U=1
