Matrix Notation and Definitions
Simple Explanation
A matrix is a rectangular array of numbers arranged in rows and columns. Its order (or size) is written mĆn, meaning m rows and n columns. Each number is called an entry (or element), identified by its row and column position, aįµ¢ā±¼. Special types include the square matrix (same number of rows and columns), the zero matrix (every entry 0), and the identity matrix (1s down the main diagonal, 0s elsewhere).
Why Do We Need It?
Matrices organize large amounts of related numbers into one single object ā the foundation for every operation and application covered in the rest of this chapter.
Worked Example
Identify a matrix's order and a specific entry
For the matrix A = [[3, 7, 1], [5, 2, 9]], state its order and find the entry aāā.
Why Does This Work?
Matrix notation is simply a precise addressing system ā writing aįµ¢ā±¼ unambiguously specifies exactly one entry, since every entry has a unique (row, column) position.
Real-Life Example
A spreadsheet of sales figures
A company records monthly sales for several products in a spreadsheet grid ā rows for products, columns for months.
That spreadsheet grid is exactly a matrix ā each cell is an entry addressed by its row and column, just like aįµ¢ā±¼.
Practice
What is the order of the matrix [[1,2],[3,4],[5,6]]?
EasyCommon mistake
Reversing rows and columns in the order notation ā mĆn always means m ROWS first, then n COLUMNS, never the other way around.
Quick Review
- A matrix is a rectangular array of numbers; its order is (rows)Ć(columns).
- aįµ¢ā±¼ addresses the entry in row i, column j.
- Special types: square, zero, and identity matrices.