MATH08057: Introduction to Linear Algebra full notes
These MATH08057 notes cover the full Introduction to Linear Algebra course at the University of Edinburgh. They are 53 pages long and clearly handwritten notes.
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About These Notes
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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