5-Matrix Algebra Page 163 Wednesday, February 4, 2004 12:49 PM
Matrix Algebra 163SUMMARY
■ In representing and modeling economic and financial phenomena it is
useful to consider ordered arrays of numbers as a single mathematical
object.
■ Ordered arrays of numbers are called vectors and matrices; vectors are
a particular type of matrix.
■ It is possible to consistently define operations on vectors and matrices
including the multiplication of matrices by scalars, sum of matrices,
product of matrices, and inversion of matrices.
■ Determinants are numbers associated with square matrices defined as
the sum of signed products of elements chosen from different rows and
columns.
■ A matrix can be inverted only if its determinant is not zero.
■ The eigenvectors of a square matrix are those vectors that do not
change direction when multiplied by the matrix.