# Four Fundamental Subspaces & Transpose - Outline * **Row space and Column space** * Linear Algebra Goodnotes, pg 11 * [Dear linear algebra students, This is what matrices (and matrix manipulation) really look like - YouTube](https://www.youtube.com/watch?v=4csuTO7UTMo&t=100s) * Ways to view a matrix (notability) * Note: fascinating that a matrix has rows and columns, so clearly there is some relationship. That can be thought of as the four fundamental subspaces * **Null space** * Remember: Null space represents portion of vector thrown out (I think the portion that is orthogonal to row space) * Breaking down a matrix via row, column, null space: * Good notes linear algebra pg 11 and up * Four fundamental subspaces & transpose * notability note * **Duality** * 3b1b interpretation * what are dual spaces? * notability: matrix transpose intuition * notability: vectors, vector spaces, tensors * [Before you continue to YouTube](https://www.youtube.com/playlist?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG) * --- Date: 20220612 Links to: Tags: #review References: * []()