How to get vectors y such that y* A = 0?

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Lucas Medina 2015-7-16

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编辑： John D'Errico 2015-7-16

I know that normally, you would do something like [W,D] = eig(A.') and then the rows of W.' are the left eigenvectors "y" of A such that yA = 0.

However, this is not what I want. I'm trying to find column vectors y with the following property: y* A = 0, where * is the conjugate transpose . How would I do this using eig?

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Answer 1

John D'Errico 2015-7-16

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编辑：John D'Errico 2015-7-16

在 MATLAB Online 中打开

Nope. You would NOT use eig, since eig solves a different problem. Why use the wrong tool to solve a simple problem?

You need to find the vectors that lie in the null-space of the columns of A. For example...

A = randn(5,3) + i*randn(5,3);
N = null(A');
N'*A
ans =
  -5.5511e-17 - 3.9552e-16i  -9.7145e-17 + 8.3267e-17i  -2.7756e-17 - 4.8572e-17i
   2.3592e-16 - 2.2204e-16i   6.9389e-18 - 1.1102e-16i   3.5388e-16 - 4.4409e-16i

N is a column matrix, here with two columns. See that the transpose of those columns, when left multiplied times A, yields zero. Don't forget that ' is indeed a conjugate transpose, as you desired.