linear map

An important special case is the kernel of a linear map.

Both examples have the property that any continuous linear map to the real numbers is 0.

A single linear map may be represented by many matrices.

The matrix of the linear map T is necessarily square.

No classification of linear maps could hope to be exhaustive.

Here is the vector space of linear maps from to .

Let be given by and a linear map.

We can define a continuous random field well enough as a linear map from a space of functions into the real numbers.

There is a simple way to make precise sense of differentials by regarding them as linear maps.

A linear map is a homomorphism between two vector spaces.

If X is infinite-dimensional, there exist linear maps which are not continuous.

Discontinuous linear maps can be proven to exist more generally even if the space is complete.

The class of convex cones is also closed under arbitrary linear maps.

Let be the linear map satisfying for all .

The uniform and strong topologies are generally different for other spaces of linear maps; see below.

The conclusion is that, intuitively, consists of a translation and a linear map.

An important result about dimensions is given by the rank-nullity theorem for linear maps.

This article deals with linear maps from a vector space to its field of scalars.

Since , the linear map has the two eigenvalues .

The map from to is a compact linear map.

If such a linear map u exists, then f is said to be quasi-differentiable at x.

In infinite-dimensional spaces, not all linear maps are continuous.

Indeed every linear map can be converted into a semilinear map in such a way.

The tensor product also operates on linear maps between vector spaces.

For example, a linear map can be represented by a matrix, a 2-dimensional array, and therefore is a 2nd-order tensor.