Notes on linear algebra by J. Calder. Work in progress, read at your own risk.

• The Spectral Theorem, slowly

  On why self-adjoint operators are nothing more than oriented stretches.
  May 4, 2026Spectral Theory
• Determinants are volume, signed

  How I stopped memorizing the cofactor formula.
  Apr 22, 2026Determinants
• Dual spaces: a brief crisis

  Three days lost, one diagram regained.
  Apr 9, 2026Dual Spaces
• Eigenvalues as fixed directions

  Notes on what survives a transformation.
  Mar 27, 2026Eigenvalues
• Change of basis is a Rosetta stone

  The same operator, three alphabets.
  Mar 14, 2026Linear Maps
• Rank–nullity, as bookkeeping

  Nothing is lost; dimension is a ledger.
  Feb 28, 2026Linear Maps
• Inner products gave me geometry back

  Why angles only exist after you choose a form.
  Feb 12, 2026Inner Products
• Polynomials of an operator

  On the algebra hiding inside a linear map.
  Jan 30, 2026Operators
• A small grudge against Axler

  And why I forgive him by chapter four.
  Jan 12, 2026Notebook
• Linear independence is just non-redundancy

  The simplest idea, dressed in formal clothes.
  Dec 28, 2025Bases
• Vector spaces aren't really about arrows

  Functions, polynomials, sequences — they all fit.
  Dec 15, 2025Vector Spaces
• Why I am studying alone

  Notes from before any of this began.
  Nov 30, 2025Notebook