# Inverse, Column space and null space

# Inverse

We can use **Inverse transformation** to resolve the function.

# Column space

The column sapce is the span of the columns of the matrix.

And the column space represents the rank of the matrix.

When a 3-D matrix has rank 3, we can call it **full rank**.

# Null space

For a full rank matrix only origin can be squished into origin.

But for a matrices aren’t full rank, which squish to a smaller dimension, you can have a whole bunch of vectors that land on zero.

For a 2-D matrix, if its rank is 1, it squish all the vectors on a line to the origin.

For a 3-D matrix, if its rank is 1, it squish all the vectors on a **plane** to the origin, if its rank is 2, it squish all the vectors on a **line** to the origin.

Reference

https://www.3blue1brown.com/topics/linear-algebra