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I have always thought that the best way to learn linear algebra would involve constant visualization and interaction on a computer. My LA teacher in college to
by lwb 7y ago
I have always thought that the best way to learn linear algebra would involve constant visualization and interaction on a computer.
My LA teacher in college told us that he visualized the left matrix in a matrix multiplication flipping over and crashing down on top of the right matrix. (or is that backwards?) The only way I learned things like vector spaces and orthogonality was by visualizing them in my head, Bret-Victor style.
In my totally unqualified opinion, there is a huge opportunity for a software product that allows people to play with and explore mathematical concepts in a visual and fun way.
- mkl 7y ago> the left matrix in a matrix multiplication flipping over and crashing down on top of the right matrix. (or is that backwards?) Both ways work. A row from the left matrix rotated 90° clockwise to line up with the rows of the right matrix gives you the coefficients to use to combine those rows into a row of the result matrix. Conversely, a column from the right matrix rotated 90° anticlockwise to line up with the columns of the left matrix gives you the coefficients to use to combine those columns into a column of the result matrix. I didn't fully understand that until I read Strang's book.