Linear algebra

Vectors and matrices

Physics:
Vectors are arrows pointing in space with length and direction ↗

Computer Science:
Vectors are ordered lists of numbers \begin{bmatrix} 2\,600 ft^2 \\ \300,000 \end{bmatrix}$

Mathematics:
Vectors can be anything where there’s a notion of adding two vectors, and multiplying a vector by a number

---

Vector addition: $\left[\begin{array}{c}3\\ -5\end{array}\right]+\left[\begin{array}{c}2\\ 1\end{array}\right]=\left[\begin{array}{c}3+2\\ -5+1\end{array}\right]$

Vector multiplication (scaling): $2\left[\begin{array}{c}3\\ -5\end{array}\right]=\left[\begin{array}{c}2(3)\\ 2(-5)\end{array}\right]$

---

• Matrix operations
• Eigenvalues and eigenvectors
• Vector spaces and linear transformations