Welcome to the Matrix Operations guide! 📘 This section covers fundamental matrix operations essential for linear algebra and data science. Let's dive in!
1. Basic Concepts
A matrix is a rectangular array of numbers arranged in rows and columns. 📊
- Matrix Addition: Add corresponding elements of two matrices.
- Scalar Multiplication: Multiply every element of a matrix by a scalar (single number).
- Matrix Multiplication: Multiply rows of the first matrix by columns of the second.
2. Common Operations
| Operation | Description | Example |
|---|---|---|
| Transpose | Flips rows and columns of a matrix. | $ A^T $ for matrix $ A $ |
| Determinant | A scalar value of a square matrix. | $ \text{det}(A) $ |
| Inverse | A matrix that undoes another matrix. | $ A^{-1} $ for invertible $ A $ |
3. Applications
Matrices are used in:
- Computer graphics 🖼️
- Machine learning 🤖
- Physics and engineering ⚙️
For deeper insights into matrix multiplication, check out our Matrix Multiplication Guide. 📚
4. Practice
Try solving these problems:
- Add two 2x2 matrices.
- Multiply a 3x3 matrix by a scalar.
- Find the inverse of a diagonal matrix.
Explore more with our Linear Algebra Resources. 🔗