hw$9.$m $($Function$)$

Problem $3$: Write a function that can be called as

lambda$\_$vec, $U$ my$\_$subspaceiteration $($Afun$,W0,$ maxiter,, tol$)$

implementing subspace iteration for the dominant $k$ eigenpairs of a symmetric $nn$

matrix $A($including the Rayleigh$-$Ritz step, for which you may call the built$-$in Mat

lab function eig on a smaller $kk$ matrix$).$ The input Afun is a function handle

which, when called as Afun$($V$)$ for a matrix $V$ with $n$ rows, returns $AV.$ The input

WO is an arbitrary initial guess for subspace iteration. The number $k$ of columns in

the initial guess dictates the number $k$ of dominant eigenvectors we seek. The outpu

lambda$\_$vec is a vector of the $k$ dominant eigenvalues, ordered non$-$increasingly, and

the columns of the output $U$ are the corresponding dominant eigenvectors.

Use your function to run PCA on the data matrix Y from hw$9.$mat. The array Y

is $mn,$ where $m$ indicates the data dimension and $n$ indicates the number of dat

points. You will have to de$-$mean Y yourself to produce a data matrix X with zer

points. You will have to de$-$mean Y yourself to produce a data matrix X with zero

appropriate function handle implementing matrix multiplication by $x{x}^{TT}$ via

Afun $=$@$(W)x**(x^{\text{'}}**(W)).$ Make sure to answer all parts and provide the correct MATLAB code. Met me know if there is anything I need to revise!