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## Main Question or Discussion Point

Hi all. I'm studying from Leon's Linear Algebra with Applications. I'm wondering if one of his examples has an error.

In Application 2, he's talking about searching databases. He says we should imagine a database of m documents and n possible search words. Then he says that this can be put into an mxn matrix in which each column represents a book-- the jth entry of the column is 1 if that book contains the word, 0 if it doesn't.

He then says a "search vector" lives in R^m, and it's a column vector whose jth entry is 1 if you are seraching for that word.

Does he have his m's and n's mixed up? It seems to me like if you have m documents and each column of the matrix represents one, you need an nxm matrix. Similarly, you can't search through n words by using a vector in R^m, correct? Does he mean you take an nxm matrix and multiply its transpose by the vector in R^n?

In Application 2, he's talking about searching databases. He says we should imagine a database of m documents and n possible search words. Then he says that this can be put into an mxn matrix in which each column represents a book-- the jth entry of the column is 1 if that book contains the word, 0 if it doesn't.

He then says a "search vector" lives in R^m, and it's a column vector whose jth entry is 1 if you are seraching for that word.

Does he have his m's and n's mixed up? It seems to me like if you have m documents and each column of the matrix represents one, you need an nxm matrix. Similarly, you can't search through n words by using a vector in R^m, correct? Does he mean you take an nxm matrix and multiply its transpose by the vector in R^n?