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**Why the name "singular"?**

The textbook I am currently reading gives the following definition:

"A square matrix is nonsingular if it is the matrix of coefficients of a homogeneous system with a unique solution. It is singular otherwise."

As I understand it a homogeneous system will either have one or

infinitely many solutions and I assumed this is where the choice of

the word singular came from. But if this is the case then the definition

seems backwards. Because the use of the word singular is consistent

in the book I think the definition is not backwards, just my understanding

of the word singular is.

So I went online to try to figure out what singular is describing.

Unfortunately the vast majority of the hits where related to determinates

and matrix inverses. Topics which I have not yet covered.

From the reading I did do I believe an inverse is roughly, a way to get back

to where you came from. So a matrix that can be applied but not unapplied is also singular. This seems like it is probably the significant fact but I am missing the connection to the word singular.

Could someone please explain what the word "singular" is describing?