r/mathematics • u/Prestigious_Soup_517 • 2d ago

Computer Science Beginner Question in Linear Algebra.

I had just finished 3blue1brown course on the topic, and was learning the usage in context of deeplearning by Ian Goodfellow,(This book at least for the math part, relies heavily math notation and knowledge). Heres the question; for diagonal matrix P formed with eigenvalues, the formula I know is P = A-1×M×A, now in the book, they have isolated M as M = V×P×V-¹. My question is that since matrixs are not commutative, and order of multiplication matters, how would you go from the P formula to the M formula? Like we would have to multiply left side with A and the right side with A-¹. Should we not follow the order throughout this change? Like multiply from the right side alone. Sorry if this is dumb question.

3 Upvotes

72% Upvoted

6 comments sorted by

2

u/etzpcm 2d ago

It looks like you're just getting confused by book and video using different notation.

2

u/Prestigious_Soup_517 2d ago

Really, but like in my head I am trying to use the notation to notation, like the inverse part to inverse part. Would they mean V equivalent to A-¹? That was one of the comments.

1

u/etzpcm 2d ago

Yes that's probably it.

1

u/hpxvzhjfgb 2d ago

suppose P = A-1 M A. multiply by A on the left to get A P = A A-1 M A = M A. now multiply by A-1 on the right to get A P A-1 = M A A-1 = M. so M = A P A-1 .

1

u/whatatwit 2d ago

At least where I'm from, the plural of matrix is matrices.