Linear Algebra
maths ✒ linear algebra
Inner Product
Defintions/topics to learn
quotient spaces rank nullity theorem = first isomorphism theorem direct sum of subspaces projection operators T-invariance partition of the identity linear functional dual space dual basis annihilator dual of dual space dual transformation --- determinant and trace characteristic polynomial minimal polynomial eigenvalues, eigenvectors linear transformations form a vector space minimal polynomial exist and is unique primary decomposition theorem (mark 1) primary decomposition theorem (mark 2) primary decomposition theorem (mark 3) condition for diagonalisability triangular form Cayley-Hamilton theorem real inner-product space orthogonal set ortonormal basis complex inner-product space Gram-Schmidt process Bessel's inequality Cauchy-Schwarz Inequality Isometries of inner product spaces Riesz Representation Lemma --- Adjoints of linear transformations Self-adjoint linear transformations Eigenvalues and eigenvectors of self-adjoint linear transformations Diagonalisability and the spectral theorem for self-adjoint linear transformations Spectral theorem Quadratic forms Sylvester's Law of Inertia
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