Abstract Homogeneous strain can be computed most easily by the methods of matrix algebra. Lines, planes and ellipsoids represented in matrix form can be homogeneously deformed by simple matrix multiplication by linear transformation matrices, the elements of which are the coefficients of the transformation equations. Deformation matrices or linear transformation matrices which cause geological-type homogeneous strain are divided into four classes based on the presence or absence of symmetry and/or orthogonality. The nature of the homogeneous strain caused by each class of deformation matrix is examined. Orthogonal-symmetrical and orthogonal matrices cause rotation. Symmetrical matrices cause irrotational strain with co-axial strain as a special case. Matrices which are neither orthogonal nor symmetrical cause many different types of rotational strain, some of which are examined.