Hello all. This is my first post here. Hope someone can help. Thank you guys in advance.(adsbygoogle = window.adsbygoogle || []).push({});

Here is the question:

I have a n-by-n matrix A, whose eigenvalues are all real, distinct. And the matrix is positive semi-definite. It has linearly independent eigenvectors V_1...V_n. Now I have known part of them, let's say V_1...V_m. How can I get a basis for span{V_(m+1)...V_n} without calculating V_(m+1)...V_n (because n may be large and calculating all the eigenvectors is unfeasible)?

To better illustrate the question, here is a working example. Let's say

A=[1 1 -1;

0 2 1;

0 0 3;]

whose eigenvalues and eigenvectors are:

lamda_1=1, V_1=[1 0 0]'

lamda_2=2, V_2=[1 1 0]'

lamda_3=3, V_3=[0 1 1]'

If I only know lamda_1 and V_1 now, how can I get a basis for span{V_2,V_3} without calculating V_2 and V_3?

Thanks again and I appreciate your help!

Sincerely,

Zach

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# How can I find a basis for the span of some eigenvectors?

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