Page 80 - Excel for Scientists and Engineers: Numerical Methods

Chapter 3

Worksheet Functions

for Working with Matrices

Arrays, Matrices and Determinants

Spreadsheet calculations lend themselves almost automatically to the use of
arrays of values. Arrays in Excel can be either one- or two-dimensional. For the
solution of many types of problem, it is convenient to manipulate an entire
rectangular array of values as a unit. Such an array is termed a matrix. (In Excel,
the terms "range," "array" and ''matrix'' are virtually interchangeable.) An rn x n
matrix (m rows and n columns) of values is illustrated below:

The values comprising the array are called matrix elements. Mathematical
operations on matrices have their own special rules, to be discussed in the
following sections.

Some Types of Matrices
A matrix which contains a single column of m rows or a single row of n
columns is called a vector.
A square matrix has the same number of rows and columns. The set of
elements aij for which i = j (all, a22, ..., a,,,,) is called the main diagonal or
principal diagonal.
If all the elements of a square matrix are zero except those on the main
diagonal, the matrix is termed a diagonal matrix. A diagonal matrix whose
diagonal elements are all 1 is a unit matrix.

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