The theory of representations: symmetries and linear groups

In the vast universe of mathematics, representation theory stands out as a precious diaphragm revealing the hidden mechanisms behind groups and their symmetries. Faced with the abstraction of groups, considering how they can concretely act on vector spaces through matrices or linear transformations gives a tangible dimension to concepts that are otherwise speculative. Whether in … Read more

The study of mathematical symmetries

L'étude des symétries mathématiques

IN BRIEF Central symmetry: transformation around a point, conserving the properties of the original figure. Construction of symmetrics: procedure to obtain the symmetric of a point, segment, or figure. Centre of symmetry: a point O if its symmetric is identical to the figure. Geometric transformation: symmetry is an involutive form, preserving parallelism. Applications: symmetry is … Read more