EL590: Symmetric Matrices

Students will realize the 'ubiquity' of symmetric matrices in theory and applications (in nearly every engineering science). They understand their mathematical concepts and know how to apply them in any engineering area. Amongst other things they will master the method of 'linear squares fit' in a numerically stable manner (by help of orthogonal transformations), a method of second order approximation of plane areas (by help of conics with point symmetry), an efficient method of composition in a (imaginary quadratic class) group that is multifunctional in cryptography.

Students are capable of computations and argumentations in a mathematical due form.

Students are capable of making issues accessible by themselves.

The course enhances students to verbalise issues and participate in discussions on them.

• Properties and Classification of Symmetric Matrices / Quadratic Forms;
• Quadrics / Conics with external point of symmetry;
• The orthogonal group (important for numerical analysis);
• Local extrema of real-valued functions of several variables;
• Least Squares Fit in a numerically stable way;
• Computation of Plane Areas (Second Order Approximation);
• A-priori-computation of mutiple linear regression coefficients;
• Composition in imaginary-quadratic class groups (for Cryptography);

Fundamentals of Linear Algebra

• D. Serre: Matrices (Theory and applications). 2nd. ed., Springer (2010)
• J. Buchmann/U. Vollmer: Binary Quadratic Forms: An Algorithmic Approach. Springer (2007)
• J.W.S. Cassels: Rational Quadratic Forms. Academic Press, London (1978)