The motivation and definition of Matrix Multiplication

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Learning Objectives:
1) Describe composition of transformations, particularly the dimensions of the various domains and codomains
2) Algebraically manipulate the composition of transformations using the definition of Matrix-Vector product
3) Define Matrix-Matrix multiplication
4) Identify the allowable dimensions of matrices that can be multiplied.

This video is part of a Linear Algebra course taught at the University of Cincinnati.

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It feels amazing to finally understand why Matrix Multiplication is defined the way it is. Thank you.

kingwoomy
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marvelous. you made this easy to understand.

shakennotstired
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I don't fully understand this, I keep getting lost in what "living in Rn / Rp / Rm" actually means... can anyone explain this to me simply, or is there some video I can watch? Don't even know what to search for to find the answers... thx!

Monteyzor
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Isnt b the vector, you said its a column of the matrix

bleedgreen
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me: *sees TB*


also me: TUBERCULOSIS

Zephyr-tghu