Every square matrix has associated with it a special
number called its determinant. Although a bit complicated to define, determinants
turn out to be very useful in many contexts, from deciding if a matrix
has an inverse (and finding it) to doing geometry (finding the equation of
a circle through three points, for example).
In this learning object, you will look at
- How to define a determinant formally, in terms of its signed elementary products,
- How to use the formal definition to calculate simple determinants and to derive rules for calculating determinants,
- How to use row and column operations on determinants to simplify evaluating them.
Prerequisites: You should know a
little about matrices, especially square ones, and how to calculate with
them (see Matrices and Matrix Calculations for
further information). For the last page, you should also know how to row
reduce a matrix. You can learn how to do that from the learning object How
to Row Reduce a Matrix.
Keywords: elementary product, determinant definition, diagonals method,
triangular matrices, row operations, column operations.
The Formal Definition of a Determinant |
|||
| Introduction | The formal definition of a determinant | Determinants of special matrices | Using row and column operations on determinants |
Go
to the 
Go
to the