2008LAMAA
Topics
- Linear and multilinear algebra
- Matrix analysis
- Matrix theory
- Algebraic and differential matrix equations
- Generalized inverses
- Matrix functions. Versal Deformations
- Manifolds of matrices and vector subspaces
- Linear systems with control
- Matrix pencils
- Matrix of polynomials and rational fractions.
- Canonical forms of matrices: Jordan, Kronecker, Brunovsky, Hermite, Popov, Wiener-Hopf, Arnold, etc..
- Algebraic geometry and linear algebra
- Inverse problems of matrices: eigenvalues, completion
- Polynomials of one and several variables. Zeros of polynomials.
- Numerical linear algebra. Linear systems. Eigenvalues. Algorithms. Dense and sparse matrices. Optimization
- Singular values of matrices. Data mining. Semantic search. Images. Signals.
- Spectral perturbation of (structured) matrices.
- Pseudospectra of matrices. Pseudozeros of polynomials. Condition numbers.
Greatest common divisor of empirical polynomials.
- Cryptography. Codes. Linear systems.
- Linear algebra on commutative rings
- Symbolic linear algebra
- Defined positive matrices. Linear matrix inequalities (LMI)
- Nonnegative matrices. Graph theory. Positive control.
- Combinatorial matrix theory. Spectra and digraphs
- Totally positive matrices
- Orthogonal polynomials
- Matrices with structure: Toeplitz, Hankel, circulant, Hessenberg, etc.
- Random matrices
- Applications of the matrix theory: physics, chemistry, engineering, mechanics, biology, medicine, ecology, etc..
- Computer-aided geometric design
- Teaching of linear algebra
- History of linear algebra
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