1. Vector Spaces slides
    • A little history of Linear Algebra.
    • From Fileds to stacked structures
    • How Descartes open the door to such representations
    • Recognizing sub-spaces
    • Relation between coordinates and basis
    • Some applications
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  2. Linear Equations slides
    • The Beginning of everything
      • How we did have an idea but Descartes open the door.
    • Gauss-Jordan as Elmentary Matrix Multiplications
    • Solving \(Ax=y\)
    • Homogeneous and in-homogeneous systems
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  3. Square Matrices slides
    • The inverse of a matrix
    • Solution to \(Ax\)
    • Algorithms for inverting a matrix
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  4. Basis and Eigenvectors slides
    • The Norm as a metric
    • The Row and Column Space
    • Fundamental Theorem of Linear Algebra
    • Projections
    • Solving the Least Squared Error
    • Gram Schmidth Process
    • QR Decomposition
    • Defining eigenvectors and eigenvalues
    • Finding them
    • On the existence of Eigenvalues
    • Interesting Derivations
    \[\]
  5. Linear Transformation slides Expanding the slides
    • Introduction
    • The Algebra of Linear Transformations
    • Isomorphism
    • Representng Transformations
    • Functionals
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  6. Elementary Cannonical Forms
    • Characteristic Values
    • Annihilating Polynomials
    • Invariant Subspaces
    • Direct-Sum Decomposition
    • Invariant Direct Sums

  7. Jordan Forms

    \[\]
  8. Inner Product
    • Introduction
    • Linear Functionals
    • Unitary Operators
    • Normal Operators

UNDER CONSTRUCTION