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Comment by leni536 | Hacker News Reader

I'm a physicist and I hate to say that I'm stuck on the first equation in the first lemma. Can anybody clarify what the following notation means?

    \det(B\quad v_n)

For the determinant to make sense its argument needs to be an m×m matrix. B is an n×(n-1) matrix, v_n is an n dimensional vector.

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The blog post https://terrytao.wordpress.com/2019/08/13/eigenvectors-from-... is very readable and interesting

There's a comment with your exact question and the answer "It’s not multiplication, it’s concatenation: stick the column vector after the last column of B to “complete the square”."

As you are saying, B misses a column to be square. That column is filled with v_n. B and v_n are simply concatenated.

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