Unit · year 2
MU-202 · Linear Algebra II
Threads structure6 theorems
Abstract vector spaces, operators, and the canonical forms that classify them.
Theorems in this unit
T-046
Invariance of dimension
Every basis of a vector space has the same cardinality.
T-047
The spectral theorem
A self-adjoint operator has an orthonormal basis of eigenvectors.
T-048
The Cayley–Hamilton theorem
Every matrix satisfies its own characteristic polynomial.
T-049
The Jordan normal form
Every operator over C is similar to a direct sum of Jordan blocks.
T-050
The singular value decomposition
Any matrix factors as a rotation, a scaling, and a rotation.
T-051
The orthogonal projection theorem
Best approximation in an inner product space is orthogonal projection.