1.ya.19 Linear spaces
Condition: Let's call a square matrix \( C \) of order \( n \) 'totally commutable' if \( \forall X \) is true: \( C X=X C \), where \( X- \) is a square matrix of order \( n \). a) Is the set of such matrices a linear space? b) When Vasya said such a definition in the exam, he was told that he could not stake out the 'totally permutable' definition for a given class of matrices, because this class is already called differently. How?
Linear spaces, subspaces. Investigation of given sets with operations defined on them to compose a linear space. Axioms of linear spaces. Linear spaces of polynomials, matrices, vectors, functions and numbers.