Chapter 31: R Matrices

Part 1: What is a Matrix?

A matrix is a two-dimensional rectangular data structure where all elements must be of the same type (all numbers, all characters, all logical values, etc.). It has rows and columns, and you can think of it as a vector arranged in a grid.

Key Characteristics of Matrices

1. Two-dimensional – Has both rows and columns

2. Homogeneous – All elements must be the same type

3. Rectangular – All rows have the same length, all columns have the same length

4. Indexed – Elements can be accessed by row and column positions

Part 2: Creating Matrices

Using matrix() Function

The most common way to create a matrix is with the matrix() function:

Output of mat1 (column-major):

Output of mat3 (row-major):

Creating from Vectors

Creating Special Matrices

Adding Row and Column Names

Part 3: Matrix Properties

Basic Information

Part 4: Accessing Matrix Elements

By Index Positions

By Row and Column Names

By Logical Conditions

Part 5: Matrix Operations

Arithmetic Operations

Matrix Multiplication

Matrix Functions

Part 6: Modifying Matrices

Changing Elements

Adding Rows and Columns

Removing Rows and Columns

Combining Matrices

Part 7: Advanced Matrix Operations

Applying Functions to Rows/Columns

Sweep Function

Outer Product

Eigenvalues and Eigenvectors

Part 8: Practical Examples

Example 1: Grade Book

Example 2: Image Processing (Simplified)

Example 3: Correlation Matrix

Example 4: Linear Regression from Scratch

Part 9: Matrix vs Data Frame

Part 10: Common Mistakes and How to Avoid Them

Mistake 1: Confusing Matrix Multiplication with Element-wise Multiplication

Mistake 2: Forgetting that Matrices are Column-Major

Mistake 3: Indexing Out of Bounds

Mistake 4: Not Preserving Matrix Structure

Mistake 5: Incompatible Dimensions for Operations

Summary: The Matrix Philosophy

Matrices are your go-to structure for numerical computing in R. Master these concepts:

Creating matrices:

• matrix() with nrow and ncol

• rbind() and cbind() for combining vectors

• Special matrices: diag(), matrix(0,), matrix(1,)

Accessing elements:

• [row, col] notation

• Row names and column names for readability

• Logical indexing for conditions

Matrix operations:

• Element-wise: +, -, *, /

• Matrix multiplication: %*%

• Transpose: t()

• Inverse: solve()

• Determinant: det()

• Eigendecomposition: eigen()

Key functions:

• dim(), nrow(), ncol()

• rowSums(), colSums(), rowMeans(), colMeans()

• apply() for custom operations

• sweep() for broadcasting

Best practices:

• Use byrow = TRUE when you want row-major order

• Use drop = FALSE to preserve matrix structure

• Check dimensions before matrix multiplication

• Remember that matrices are homogeneous

• Use matrices for numerical computations, data frames for mixed data

Matrices are the foundation of numerical computing in R. They’re efficient, powerful, and essential for everything from simple statistics to complex machine learning algorithms. Master matrices, and you’ll have a solid foundation for advanced R programming!

Would you like me to elaborate on any specific aspect of matrices or explore more advanced matrix operations?