These MATH08057 notes cover the full Introduction to Linear Algebra course at the University of Edinburgh. They are 53 pages long, clearly handwritten week by week notes. I have covered all 10 weeks of lectures in these MATH08057 notes. They are comprehensive and colour coded for ease recognition. There are examples where necessary for the better understanding of a fact or a point.
Following major topics are covered within these Introduction to Linear Algebra course notes:
- Gaussian Algebra
- Elementary Operations
- Parametric Form
- Systems of Linear Equations
- Row Echelon Form
- Rank
- Homogenous Equations
- Linear Combinations
- Matrices
- Inverse of a Matrix
- Vector Dot Product
- Vector Cross Product
- Linear Transformations
- Composite Functions
- Smith Normal Form
- Geometry
- Rotations
- Reflections
- Projections
- Determinant and Trace
- Diagonalisation
- Eigenvectors and Eigenvalues
- Characteristic Polynomial
- Invariance
- Multiplicity
- Orthogonality and Orthogonal Sets
- Planes
- Subspaces
- Span
- Spanning Sets
- Linear Independence and Dependence
- Dimension
- Null-space and Eigenspace
- Normalisation
- Expansion Theorem
- Row space
- Column Space
- Rank Theorem
- Similar Matrices
- Symmetric Matrices
- Orthogonal Complements
- Gram Schmidt Algorithm
- Principle Axes
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