Linear maps

#linear map #definition #examples

#matrix representation #canonical basis #linear map

#kernel #linear map #basis

#kernel #basis #linear map

#image #linear map #generators

#rank #image dimension #matrix

#rank-nullity #rank #kernel dimension

#injectivity #kernel #linear map

#surjectivity #rank #linear map

#isomorphism #inverse #linear map

#inverse #endomorphism #matrix inverse

#composition #matrix product #representation

#composition #matrix product #linear maps

#composition #kernel #inclusion

#composition #image #inclusion

#rank #composition #inequality

#rank #invertible matrices #invariance

#change of basis #matrix representation #similarity

#similarity #trace #determinant #rank #characteristic polynomial

#projection #idempotence #kernel and image

#symmetry #involution #linear map

#nilpotent #kernel #image

#kernel #image #direct sum #endomorphism

#orthogonal projection #linear map #kernel and image

#kernel #image #transpose #orthogonal complement

#eigenvectors #injectivity #kernel

#diagonalization #eigenspaces #dimension

#invariant subspace #endomorphism #restriction

#quotient space #induced map #well-defined