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Rank

#linear-algebra #matrix #fundamental

Definition

How much information a matrix really holds. The number of linearly independent columns.

Notes

This is a bulk of Caitlin’s doctoral work. I’m not quite the specifics, but when I went to all her talks. It’s a lot of full-rank this, full-rank that.

Full rank

The rank of the matrix is the same size as the smallest dimension

From solving a linear system point of view, when the square matrix is rank deficient, it means that we do not have complete information about the system, ergo we cannot solve the system.