Orthogonal linear maps are generalizations of orthogonal matrices. By definition, a linear map \(f\) over an inner product real vector space \(V\) is an orthogonal linear map (function, or transformation) if it preserves the inner product, i.e. for all vectors \(u\) and \(v\) in \(V\), we have $$ f(u) \cdot f(v) = u \cdot v.$$…

# Tag: linear functions

## Linear maps in vector spaces

In this post, we introduce general definition of vector spaces and the linear maps between them. In the post on the finite-dimensional real vectors, we discussed their addition and subtraction, multiple of vectors by numbers, their linear combination, their independence, their dot product, their length and distance, and the angle between them. Real vector spaces…