Invariants of tensors
Concept in multilinear algebra and representation theory / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Invariants of tensors?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In mathematics, in the fields of multilinear algebra and representation theory, the principal invariants of the second rank tensor are the coefficients of the characteristic polynomial[1]
- ,
where is the identity operator and represent the polynomial's eigenvalues.
More broadly, any scalar-valued function is an invariant of if and only if for all orthogonal . This means that a formula expressing an invariant in terms of components, , will give the same result for all Cartesian bases. For example, even though individual diagonal components of will change with a change in basis, the sum of diagonal components will not change.