Matrix Algebra for SSA

I. Borg and J. Lingoes
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I. Borg: Justus-Liebig-Universität, Department of Psychology
J. Lingoes: University of Michigan, Computing Center

Chapter 17 in Multidimensional Similarity Structure Analysis, 1987, pp 270-291 from Springer

Abstract: Abstract A systematic introduction to matrix algebra is given, starting with the solution of a linear equation system. It is seen that the Gauss algorithm decomposes a scalar-product matrix B into the product XX’. If X is real, it is a solution to the representation problem for scalar products. The coordinates in X can then be rotated in some way. Another decomposition, which leads directly to coordinates relative to principal components, is closely related to the algebraic eigenvalue problem.

Keywords: vertical and horizontal matrix; matrix addition; matrix multiplication; conformable matrices; pre- and post-multiplication; multiplication from the right /left; identity matrix; rank of a matrix; full rank; linear equation system; column and row vector; algebraic operations; elementary row operations; elementary row transformations; row-echelon form of a matrix; pivot element; back substitution; neutral operation; matrix inversion; linear dependency; linear combination; regular matrix; transposition of a matrix; imaginary coordinate axis; axioms of scalar products; Choleski factor; singular matrix; permutation matrix; triangular matrix; LDU decomposition of a matrix; transformation matrix; rotation matrix; alibi and alias interpretation of linear transformations; orthogonal matrix; principal component orientation; eigenvalue; eigenvector; eigendecomposition of a matrix; determinant; oriented measure; hypervolume; normalized (normed) vector; characteristic equation; repeated (multiple) eigenvalues; symmetric matrix; spectral decomposition; power method; reflection (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-1-4612-4768-5_17

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