Search Results for ""

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

A matrix used in the Jacobi transformation method of diagonalizing matrices. The Jacobi rotation matrix P_(pq) contains 1s along the diagonal, except for the two elements ...

The turning of an object or coordinate system by an angle about a fixed point. A rotation is an orientation-preserving orthogonal transformation. Euler's rotation theorem ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

An infinitesimal transformation of a vector r is given by r^'=(I+e)r, (1) where the matrix e is infinitesimal and I is the identity matrix. (Note that the infinitesimal ...

Rodrigues' rotation formula gives an efficient method for computing the rotation matrix R in SO(3) corresponding to a rotation by an angle theta about a fixed axis specified ...

A n×n matrix A is an orthogonal matrix if AA^(T)=I, (1) where A^(T) is the transpose of A and I is the identity matrix. In particular, an orthogonal matrix is always ...

The shear matrix e_(ij)^s is obtained from the identity matrix by inserting s at (i,j), e.g., e_(12)^s=[1 s 0; 0 1 0; 0 0 1]. (1) Bolt and Hobbs (1998) define a shear matrix ...

A matrix for which horizontal and vertical dimensions are not the same (i.e., an m×n matrix with m!=n).

A square matrix A such that A^2=I, where I is the identity matrix. An involutory matrix is its own matrix inverse.