# Can an isomorphism between two finite-dimensional linear spaces be always represented by a matrix?

Is that true? Any counter-example?

• any linear transformation, isomorphism or not, can be represented by a matrix (which is finite if the dimensions are finite). Nov 4 '15 at 9:56
• An isomorphism is simply an invertible linear map from one vector space to another, and hence, can be represented by a matrix. Nov 4 '15 at 9:59