Glossary
Dimensions (of a matrix)
The size of a matrix, described by the number of rows (n) and the number of columns (m).
Example:
A spreadsheet with 5 rows and 3 columns of data has dimensions of 5x3, meaning it has 5 rows and 3 columns.
Dot product (or scalar product)
A mathematical operation that takes two vectors and returns a single scalar number, calculated by multiplying corresponding components and summing the results.
Example:
If vector A = [1, 2] and vector B = [3, 4], their dot product is (13) + (24) = 3 + 8 = 11.
Matrix
A rectangular array of numbers, symbols, or expressions arranged in rows and columns, used for mathematical operations like solving equations or transformations.
Example:
In a video game, a 3x3 matrix could represent the positions of obstacles on a 2D map, where each element (row, column) indicates if a spot is clear or blocked.
Matrix compatibility rule
A specific condition for matrix multiplication stating that the number of columns in the first matrix must equal the number of rows in the second matrix.
Example:
To multiply a 2x3 matrix by a 3x5 matrix, the inner dimensions (3 and 3) match, satisfying the matrix compatibility rule, which means the multiplication is possible.
n x m matrix
A notation used to describe a matrix that has 'n' rows and 'm' columns.
Example:
A matrix representing student grades for 4 assignments for 3 students would be a 3x4 n x m matrix, with 3 rows for students and 4 columns for assignments.