Week 15

Question 1

Symmetric Matrix?

Answer 1

if a matrix has eigenvalues (which all square matrices do) and its kernel is always orthogonal to its range, then the matrix must be symmetric.

Question 2

For symmetrical matrix, how to get matrix A B->B

Answer 2

• if the base belongs to the transformation e.g. (the Range) , multiply by the eigenvalue

-for kernel we multiply the eigenvector of kernel by it’s eigenvalue

Question 3

∇ f( x,y)

Answer 3

-partial derivatives of each, sub in then transposed

Question 4

Bottom value for normal vector of tangent plane in R^2?

Answer 4

-1

Question 5

slope of d?

Answer 5

vertical displacement/ horizontal distance

^we can use the vectors in d

Question 6

Unit vector when gradient is same direction as directional derivative (rate of increase is max)

Answer 6

u = gradient of f / mod gradient of f

Question 7

Unit vector when gradient is opposite direction as directional derivative (rate of decrease is max)

Answer 7

u = - gradient of f / mod gradient of f

Question 8

Unit vector when gradient is opposite direction as directional derivative (no rate)

Answer 8

orthogonal unit vector to rate of increase/decrease is max

Question 9

Directional derivative?

Answer 9

∇ h(ab) u / ll u ll