THE GRAM-SCHMIDT PROCESS
The Gram-Schmidt Process produces an orthogonal basis for a nonzero subspace of . It is based on the following theorem. Theorem Let be a basis for a nonzero subspace W of and: . Then is an orthogonal basis forRead More
DIAGONALIZATION OF SYMMETRIC MATRICES
What is so special about symmetric matrices? While not every square matrix is diagonalizable, every symmetric matrix can be diagonalized. Diagonal matrices are easier to work with and have many fascinating properties. In addition, every symmetric matrix can be representedRead More
SIMILAR MATRICES
As discussed in the article Matrices of Linear Transformations, the matrix representing a linear transformation depends of the bases chosen for the vector spaces associated with the transformation. For example, let T be the linear transformation from to . SomeRead More
MATRICES OF LINEAR TRANSFORMATIONS
The central proposition in this article is that for every linear transformation from a vector space to another there exists a matrix that can be viewed as a representation of the transformation and the entries of the matrix depend onRead More