Discrete Mathematics Matrices Quiz and Flashcards

Study Notes

Matrix Basics

A matrix is a 2-dimensional array of numbers with rows and columns, represented by box brackets or parentheses.
A matrix is an ordered set of numbers listed in rectangular form.
The numbers in a matrix are called "entries" (or elements or components).

Matrix Dimensions and Size

The size of a matrix with m rows and n columns is called an m x n matrix, while m and n are called its dimensions.
A 3x3 matrix has 3 rows and 3 columns, with a total of 9 entries.
A 3x4 matrix has 3 rows and 4 columns, with a total of 12 entries.

Types of Matrices

A row vector is a matrix with one row.
A column vector is a matrix with one column.
A square matrix has the same number of rows and columns.
A non-square matrix has a different number of rows and columns.
A zero matrix (or null matrix) has all entries as zero, and can be of any dimension.
A zero-one matrix has entries of only 0 and 1.
A diagonal matrix is a square matrix with all entries as zero, except on the main diagonal.
A tridiagonal matrix is a square matrix with all entries as zero, except on the main diagonal and the two adjacent diagonals.
An upper triangular matrix has all entries underneath the main diagonal as zeroes.
A lower triangular matrix has all entries above the main diagonal as zeroes.
A scalar matrix has all terms on the main diagonal as equal.
An identity matrix has all entries as zero, except those on the main diagonal as ones.

Matrix Operations

Matrices can be added and subtracted if they have the same dimension (conformable).
To add or subtract matrices, corresponding entries are added or subtracted.
Matrices A and B are not conformable for addition or subtraction if they have different dimensions.

Properties of Matrix Addition

Commutative law for addition: A+B = B+A
Associative law for addition: (A+B)+C = A+(B+C)
Additive identity: A+0 = A
Additive inverse: A + (-A) = 0

Scalar Multiplication and Matrix Multiplication

Scalar multiplication: multiplying a matrix by a scalar (number) multiplies each entry by that scalar.
Matrix multiplication: the product of a row matrix and a column matrix.

Description

Learn about the fundamental concepts of matrices in discrete mathematics, including definitions, representations, and dimensions. Understand the structure and components of matrices. Get familiar with the notation and terminology used in matrix operations.