Linear transformations

Concepts

• Linear transformation 10 exercisesA linear transformation T is a function between vector spaces that preserves addition and scalar multiplication.
• Matrix of a linear transformation 10 exercisesThe matrix [T] of a linear transformation T, with respect to given bases, has as columns the images of the domain basis vectors,…
• Kernel and image 10 exercisesThe kernel ker T of a linear transformation T is the set of vectors it sends to zero; the image ImT is the set of all vectors it…
• Rank–nullity theorem 10 exercisesFor a linear transformation T with finite-dimensional domain V, the dimension of the kernel plus that of the image equals the dim…
• Change of basis 10 exercisesThe change of basis P is the passage from a vector's coordinates with respect to a basis B to its coordinates with respect to ano…