Learn and understand all key topics from Linear Algebra with lectures and targeted worked example practice problems
Sub Category
- Math
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Objectives
- Solve systems of linear equations using matrices and various methods like Gaussian vs Gauss-Jordan Elimination, row echelon forms, row operations
- Find the deteminant and inverse of a matrix, and apply Cramer's rule
- Vectors and their operations in 2D and 3D space, including addition, scalar multiplication, subtraction, representation in coordinate systems, position vectors
- Extend vectors to n-space, including norm, standard unit vectors, dot product, angle using the Cauchy-Schwarz inequality
- Orthogonality and projection using the dot product, geometric interpretation of the cross product and triple scalar product
- Real vector spaces, subspaces, linear combinations and span, linear independence, basis, dimension, change of basis, computing the transition matrix
- Row space column space and null space, basis and effect of row operations on these spaces
- Rank, nullity, fundamental matrix spaces, overdetermined and underdetermined systems, orthogonal complements
- Matrix transformations and their properties, finding standard matrices, compositions, one-to-one
- Eigenvalues, eigenvectors, eigenspaces, geometric interpretation, matrix powers, diagonalising similar matrices, geometric and algebraic multiplicity
- Complex vector spaces, eigenvalues, eigenvectors, matrices and inner product, geometric interpretation
- Inner product spaces, orthogonality, Gram-Schmidt process and orthonormal basis, orthogonal projection
- Orthogonal diagonalisation, symmetric matrices and spectral decomposition
- Quadratic forms, principal axes theorem, conics, positive definiteness
- Diagonalisation of complex matrices, Hermitian and unitary matrices, skew symmetric and sew Hermitian matrices
- Direct/iterative numerical methods, including LU and LDU factorisation, power method, least squares, singular value and QR decomposition, Gauss-Seidel iteration
- Applications, including balancing chemical equations, polynomial interpolation, solving systems of ODEs, linear regression, and approximating functions
Pre Requisites
- Basic algebra
- Minimal Calculus 2 (integration and ordinary differential equations) knowledge for some of the applications (last section)
FAQ
- Q. How long do I have access to the course materials?
- A. You can view and review the lecture materials indefinitely, like an on-demand channel.
- Q. Can I take my courses with me wherever I go?
- A. Definitely! If you have an internet connection, courses on Udemy are available on any device at any time. If you don't have an internet connection, some instructors also let their students download course lectures. That's up to the instructor though, so make sure you get on their good side!
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