🧮 R Matrices – Create, Access, and Operate on 2D Data

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🧲 Introduction – What Are Matrices in R?

A matrix in R is a two-dimensional data structure where all elements are of the same data type (usually numeric). Think of it as a table with rows and columns, widely used in mathematics, statistics, and machine learning for data manipulation and computations.

Unlike data frames, which allow mixed types across columns, matrices are strictly homogeneous.

🎯 In this guide, you’ll learn:

• How to create and access elements in a matrix
• Matrix operations (transpose, multiplication, etc.)
• How to subset, modify, and label matrices
• Key functions for matrix algebra in R

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🏗️ Creating Matrices in R

✅ Using matrix() Function

m <- matrix(1:6, nrow = 2, ncol = 3)
print(m)

🧾 Output:

     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6

✅ Parameters:

• data: vector input
• nrow, ncol: specify rows or columns
• byrow = TRUE: fill by row instead of column

m2 <- matrix(1:6, nrow = 2, byrow = TRUE)

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🎯 Accessing Matrix Elements

m[1, 2]     # Element at row 1, column 2
m[2, ]      # Entire second row
m[, 3]      # Entire third column

Exclude elements:

m[-1, ]     # Exclude first row

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🏷️ Naming Rows and Columns

rownames(m) <- c("Row1", "Row2")
colnames(m) <- c("A", "B", "C")

Access by name:

m["Row1", "B"]   # Value at Row1 and column B

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🔁 Matrix Operations

📈 Element-wise Arithmetic:

m + 1        # Add 1 to all elements
m * 2        # Multiply all elements by 2

🧠 Matrix Multiplication (%*%):

A <- matrix(c(1, 2, 3, 4), nrow = 2)
B <- matrix(c(2, 0, 1, 2), nrow = 2)
A %*% B

🔄 Transpose (t()):

t(m)

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➕ Combining and Reshaping Matrices

🔗 Bind Rows and Columns:

rbind(c(1,2), c(3,4))    # Row bind
cbind(c(1,2), c(3,4))    # Column bind

🔄 Convert Vector to Matrix:

v <- 1:9
dim(v) <- c(3, 3)

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🧠 Useful Matrix Functions

Function	Purpose
dim()	Dimensions (rows, cols)
nrow(), ncol()	Number of rows / columns
rowSums(), colSums()	Sum across rows / cols
rowMeans(), colMeans()	Mean across rows / cols
diag()	Extract or create diagonal
solve()	Solve linear equations

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🔁 Logical Operations & Subsetting

m[m > 3]    # Returns elements > 3

m[m %% 2 == 0] <- 0   # Replace even numbers with 0

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📌 Summary – Recap & Next Steps

Matrices are a key data structure for numeric computation and linear algebra in R. They provide a powerful framework for tabular data when all elements are of the same type.

🔍 Key Takeaways:

• Create matrices using matrix(), rbind(), cbind()
• Access rows/columns using [row, col] syntax
• Perform matrix multiplication with %*%
• Use built-in functions like rowSums(), t(), and solve()
• Only homogeneous data types are allowed

⚙️ Real-World Relevance:
Matrices are used in statistics (covariance, regression), machine learning (transformation, weights), and simulations requiring fast numeric calculations.

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❓ FAQs – Matrices in R

❓ What’s the difference between a matrix and a data frame?
✅ A matrix contains one data type; a data frame can hold mixed types in different columns.

❓ How do I multiply matrices in R?
✅ Use %*% for matrix multiplication and * for element-wise:

A %*% B   # Matrix multiplication
A * B     # Element-wise multiplication

❓ Can I name matrix rows and columns?
✅ Yes, with rownames() and colnames().

❓ How do I transpose a matrix?
✅ Use t():

t(matrix(1:4, 2))

❓ How can I convert a matrix to a data frame?
✅ Use as.data.frame():

df <- as.data.frame(m)

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