IIT Madras MfE 2 Lectures: Math for Electronics II
MA2101127 lectures11 weeks
Weeks
- Week 19 lecturesCourse introduction | rlc circuits & differential equations · Real & complex numbers | scalars & fields in linear algebra · Vectors, linear equations & linear combinations in __ · Span of a set of vectors in r_ – part 1 | linear algebra foundations · Span of a set of vectors in r_ – part 2 | elimination & row reduction · Vector spaces & subspaces · Linear dependence & independence of vectors · Basis & dimension of vector subspaces in r_ · Change of basis in r^2
- Week 29 lecturesLinear transformations in r_ | matrices, scaling & rotation · Linear transformation & basis in r_ · Matrix representation of a linear transformation · Linear transformations: scaling, rotation · Range, null, and rank of a linear transformation · Solving linear equations | linear algebra view · Composition of linear transformations & matrix multiplication · Inverse of a linear transformation · Change of basis
- Week 312 lecturesRecall:linear transformations · Range & null space of composed linear transformations in r_ · When is a composition zero? | rank, range & null space in linear transformations · Linear operators · Applications of operators · Scaling & rotation, basic matrix algebra & complex vector space · Eigenvalues · Eigenvectors · Properties of eigenvalues & eigenvectors · Diagonalization of a matrix · Powers of a matrix | diagonalization, jordan form & eigenvalue methods · Visualizing operators
- Week 49 lecturesInner product in r2 & c2 · Magnitude of a vector, distance between two vectors, and angle between vectors. · Orthogonal complement or dual · Inner product as a linear transformation · Adjoint of an linear operator · Range & null of an operator & its adjoint · Operations with adjoint | rules & matrix representation · Eigenvalues & eigenvectors of an operator & its adjoint · Least square fit : orthogonality principle
- Week 510 lecturesVector spaces in rn & cn · Span of vectors · Span membership · Linear dependence & independence · Spanning set & basis of f_ · Linear transformations in higher dimensions · Elimination, spanning sets & basis · Range & null of a linear transformation | part 1 · Range & null of a linear transformation | part 2 · Fundamental theorem of linear transformation
- Week 610 lecturesMatrix algebra - addition & multiplication · Matrix algebra - inverse & powers · Eigenvalues & eigenvectors · Existence of eigenvalues - proof 1 · Diagonalizability & its applications · Change of basis · Power of diagonalizable matrix · Upper triangularization · Circular convolution & circular matrix · Math for Electronics 2
- Week 77 lecturesInner product spaces · Norm of vector, orthogonal vectors, orthogonal decomposition, two inequalities · Orthonormal basis & orthonormalization · Gramm-schmidt orthonormalization · Orthonormal basis: Properties · Least square solutions · Orthogonal complement & projections
- Week 87 lecturesOperators in inner product spaces · Adjoint of a linear transformation · Four fundamental spaces · Operators & their adjoints · Self adjoint operators · Diagonalizability of self adjoint operators · Eigenvalues and Eigenvectors of operators
- Week 97 lecturesConics in 2D · Quadratic forms & symmetric matrices · Quadratic forms in c_ · Oscillation modes in system · Correlation & covariance matrix · Positive semi-definite matrices · Graph & adjacency matrix
- Week 104 lecturesCirculant matrices & the fourier basis · Discrete fourier transform (DFT) · Normal operators & matrices · Linear algebra on computer
- Week 117 lecturesSequence & function spaces · Inner product & norm in sequence & function spaces · Orthonormal basis for signal spaces · Polynomial approximations & projections in function spaces · Sinusoids, projection & introduction of fourier series · Fourier series · Complex exponential form of fourier series