The exhaustive list of topics in Matrix Theory And Linear Algebra in which we provide Help with Homework Assignment and Help with Project is as follows:

• First Basic Problem – Systems of Linear equations - Matrix Notation – The various questions that arise with a system of linear eqautions
• Second Basic Problem – Diagonalization of a square matrix – The various questions that arise with diagonalization.
• Vector Spaces
• Vector spaces
• Subspaces
• Linear combinations and subspaces spanned by a set of vectors
• Linear dependence and Linear independence
• Spanning Set and Basis
• Finite dimensional spaces
• Dimension
• Solutions of Linear Systems
• Simple systems
• Homogeneous and Nonhomogeneous systems
• Gaussian elimination
• Null Space and Range
• Rank and nullity
• Consistency conditions in terms of rank
• General Solution of a linear system
• Elementary Row and Column operations
• Row Reduced Form
• Triangular Matrix Factorization
• Important Subspaces associsted with a matrix
• Range and Null space
• Rank and Nullity
• Rank Nullity theorem
• Four Fundamental subspaces
• Orientation of the four subspaces
• Orthogonality
• Inner product
• Inner product Spaces
• Cauchy – Schwarz inequality
• Norm
• Orthogonality
• Gram – Schmidt orthonormalization
• Orthonormal basis
• Expansion in terms of orthonormal basis – Fourier series
• Orthogonal complement
• Decomposition of a vector with respect to a subspace and its orthogonal complement – Pythagorus Theorem
• Eigenvalues and Eigenvectors
• Eigenvalue – Eigenvector pairs
• Where do we look for eigenvalues – characteristic equation
• Algebraic multiplicity
• Eigenvectors, Eigenspaces and geometric multiplicity
• Diagonalizable Matrices
• Diagonalization criterion
• Diagonalizing matrix
• Cayley-Hamilton theorem, Annihilating polynomials, Minimal Polynomial
• Diagonalizability and Minimal polynomial
• Projections
• Decomposition of the matrix in terms of projections
• Hermitian Matrices
• Real symmetric and Hermitian Matrices
• Properties of eigenvalues and eigenvectors
• Unitary/Orthoginal Diagonalizbility of Complex Hermitian/Real Symmetric matrices
• Spectral Theorem
• Positive and Negative Definite and Semi definite matrices
• General Matrices
• Matrices AAT and ATA
• Rank, Nullity, Range and Null Space of AAT and ATA
• Strategy for choosing the basis for the four fundamental subspaces
• Singular Values
• Singular Value Decomposition
• Pseudoinverse and Optimal solution of a linear system of equations
• Geometry of Pseudoinverse
• Jordan Cnonical form
• Primary Decomposition Theorem
• Nilpotent matrices
• Canonical form for a nilpotent matrix
• Jordan Canonical Form
• Functions of a matrix
• Selected Topics in Applications
• Optimization and Linear Programming
• Network models
• Game Theory
• Control Theory
• Image Compression