Master Linear Algebra (Matrices, Vector Spaces, Numerical)
Learn and understand all key topics from Linear Algebra with lectures and targeted worked example practice problems
4
students
14 hours
content
Jun 2025
last update
$44.99
regular price
What you will learn
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
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6645395
udemy ID
31/05/2025
course created date
05/06/2025
course indexed date
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