• anonymous
Couldn't understand what the symbol P^ (P cap ) means in Q5.1 (b) here: Further can't understand the solution: what's the block diagonal matrix? Can't we just use the matrix in 5.1 (a) problem because P^4 = I*P = P not equal to I which is what we need?
MIT 18.06 Linear Algebra, Spring 2010
  • Stacey Warren - Expert
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
  • katieb
I got my questions answered at in under 10 minutes. Go to now for free help!
  • JoshDanziger23
P^ is just another variable: you could use Q or R or anything else but Prof Strang likes to use the letter P for permutation matrices. Here he's already used P for a (3,3) matrix so he uses P^ for a (4,4) one. A block matrix is one where you specify a whole submatrix rather than giving every single element. So [1 0; P 0] here is not a (2,2) matrix but a (4,4) one with the bottom right (3,3) elements equal to P. It turns out you can do matrix multiplication on block matrices by following the usual rules but using matrix multiplication where you have to multiply submatrices. Try it with P^.
  • JoshDanziger23
Of course I mean [1 0; 0 P]

Looking for something else?

Not the answer you are looking for? Search for more explanations.