## Chapter 26. Matrices

#### Motivation

We have seen how to use arrays to store one-dimensional lists in memory.

Often there is a need to store and manage data which is conceptually multidimensional.

##### Tables

A table is any two-dimensional arrangement of data. Common uses are timetables, score tables, etc.

Table 26.1. Time Table

SunMonTueWedThuFriSat
8:00am
9:00
10:00
11:00

##### Grids

Grids are representations of values at physical locations in two dimensions. Grids are commonly used to represent weather data.

Table 26.2. Temperature

Lat/Long86878889909192
4456545355595254
4357565860555458
4259615855565657

##### Bricks

A brick is like a grid, but with more than two dimensions. Bricks of data can represent things like MRI images, or weather data including altitude as well as latitude and longitude.

##### Systems of Equations

Systems of polynomial equations are commonly stored as a matrix of coefficients, which can then be solved using techniques such as Gaussian elimination.

##### Matrix Representation

In all of the examples above, we wish to identify one piece of data in a collection using multiple coordinates. For example, we may want to check our schedule for (Mon, 10:00), find the temperature at latitude, longitude (43o, 78o), or measure brain activity at 10mm sagittal, 8mm coronal, and 12mm transverse (10, 8, 12).

Multidimensional data can be represented as a matrix, which is a multidimensional collection of numbers. A vector, defined in Chapter 23, Arrays is a is simply a matrix where only one dimension has a measurement greater than 1. For a two-dimensional matrix, the row subscript is first by convention.

Table 26.3. Generic 2D Matrix

A =
 a1,1 a1,2 a1,3 a2,1 a2,2 a2,3 a3,1 a3,2 a3,3