Arrays, Matrices and Determinants

Spreadsheet calculations lend themselves almost automatically to the use of arrays of values. As you ve seen, 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 m x n matrix (m rows and n columns) of values is illustrated on the following page. 

The values comprising the array are called matrix elements. Mathematical operations on matrices have their own special rules. 

A square matrix has the same number of rows and columns. If all the elements of a square matrix are zero except those on the main diagonal (flu, fl22, v cinn) the matrix is termed a diagonal matrix. A diagonal matrix whose diagonal elements are all 1 is a unit matrix. 

A matrix which contains a single column of m rows or a single row of n columns is called a vector. 

A determinant is simply a square matrix. There is a procedure for the numerical evaluation of a determinant, so that anN xN 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, Solving Sets of Simultaneous Linear Equations in Chapter 10.) 

---