Matrix analysis facts for kids
Matrix analysis is a subfield of linear algebra. It focuses on analytical properties of matrices. In this subject, vector norms and matrix norms are introduced. The goal of this area is deepen understanding to matrix eigenvalues and system of linear equations. This leads to discussions in numerical linear algebra.
The following topics are studied in the context of matrix analysis:
- Discussing matrices by tools from functional analysis
- Inequalities related to matrix norms or matrix eigenvalues
- Behavior of matrix eigenvalues
Functional analysis usually discusses mathematical operators in infinite dimension Hilbert spaces. But difficulty remains even discussion is limited to matrices (which is a finite dimension mathematical operator). This is because difficulty comes not only from infinite dimension but also non-commutativity. And matrices are good examples of non-commutative mathematical operators (In other words, you cannot change the order of matrix multiplication). Matrix analysis is trying to overcome problems caused by non-commutativity.
The following results are known as remarkable achievements in this area:
- Matrix Young inequalities
- Lidskii theorem
- Hansen-Pedersen method
Matrix analysis Facts for Kids. Kiddle Encyclopedia.