Resolved: Last example in Dot Product of Matrices
Hello, I have a quick question regarding the last example in this section.
I understand why the two matrices are not compatible and therefore cannot be multiplied. But I wonder why we couldn't just switch around the two matrices to find an answer, so 2x3 times 3x4 instead of 3x4 times 2x3.
My guess is that this is not always an option depending on what our goal or project is, but if an instructor or student could give a more concrete answer or example it would be much appreciated!
Thank you :)
2 answers ( 1 marked as helpful)
Hi Lae!
Thanks for reaching out!
Please note that matrix multiplication is not commutative. This means that switching the order of the matrices generally doesn't work because it can either result in a completely different matrix or make multiplication impossible due to incompatible dimensions. The order in which you multiply matrices matters because it affects the outcome, both in terms of the dimensions of the resulting matrix and the specific values within it.
You are right in your suggestion - in many applications, the order of multiplication corresponds to the structure of a problem, thus you can't just reverse it.
Let me give you an example from the audio processing. In the digital world, a song (or an audio signal) is often represented as a vector, while the filters for modifying this song (like equalizers, or echo effects) are represented as matrices. If you decide to apply these two filters to a song - the order will matter. Applying an equalization filter (for removing particular frequencies from the song) followed by an echo effect will produce a different result than applying the echo first and then the equalization. The first order might reduce specific frequencies before adding echo, while the reversed order would blend the frequencies differently after the echo is applied, leading to a different audio output. This is how matrix multiplication order can be crucial!
I hope you find this answer helpful.
Best,
Ivan
Thank you Ivan, this was a very helpful explanation and example!