Page 81 - Excel for Scientists and Engineers: Numerical Methods

58 EXCEL: NUMERICAL METHODS

An upper triangular matrix has values on the main diagonal and above, but
the values of all elements below the main diagonal are zero; similarly, a lower
triangular matrix has zero values for all elements above the main diagonal.
A tridiagonal matrix contains all zeros except on the main diagonal and the
two adjacent diagonals.
A symmetric matrix is a square matrix in which aij = aji.
A determinant is a property of a square matrix; there is a procedure for the
numerical evaluation of a determinant, so that an N x N matrix can be reduced to
a single numerical value. The value of the determinant has properties that make
it useful in certain tests and equations. (See, for example, Tramer's Rule" in
Chapter 9.)

An Introduction to Matrix Mathematics

Matrix algebra provides a powerful method for the manipulation of sets of
numbers. Many mathematical operations, such as addition, subtraction,
multiplication and division, have their counterparts in matrix algebra. Our
discussion will be limited to the manipulations of square matrices. For purposes
of illustration, two 3 x 3 matrices will be defined, namely

and

a+q b+q c+q
Addition of a constant: A + q = d+ q e+ q f + q 1
.g+q h+q i+q

a b c
S
[g h ] [I y I]=[::: (I:]
A+B= d e f + u v a+r b+s c+t