2. Linear combinations, span and basis

Linear combinations, span and basis

What to learn

- What is the **basis**
- What is the **Linear combinations**
- What is the **span**
- What is **linear dependent** ## Description
- **basis**
    - We can express that vector  in coordination system consists of basis vector's summation and multiplication
        - Example :
            - unit vector of x direction : i, x hat
            - unit vector of y direction : j, y hat
            - Any vector can be explained like ai+bj(a,b are constants)
        - We can call scaling two vectors  and adding as **Linear Combinations**
- **Linear Combination** can makes three types in 2d coordination
    - Plane
    - Line
    - Zero
- Set of all linear combinations of given vectors is **Span**
    - So we can call above three types as **Span**
    - If we can remove one vector without shrinking of the span, we can call the vector as **linearly dependent** vector.
        - We can also say that vector is made up of linear combination of another vectors.
    - If one vector can make another dimension of the span, then we can call the vector as **linearly independent** vector. ## Next Step - Linear transformations ## References - [https://www.youtube.com/watch?v=k7RM-ot2NWY&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=2](https://www.youtube.com/watch?v=k7RM-ot2NWY&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=2)