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## Main Question or Discussion Point

Is there any difference between a vector subspace and a linear manifold.

Paul Halmos in Finite Dimensional Vector Spaces calls them the same thing.

Hamburger and Grimshaw in Linear Trasforms in n Dimensional Vector Space does not use the word subspce at all.

Planet Math says a Linear Manifold is a Linear Subspace possibly moved from the origin ( surely incorrect if it is a vector space ).

I assume the first source is correct, the second just uses a different name and the third is incorrect.

Is this so.

Thanks. Matheeinste

Paul Halmos in Finite Dimensional Vector Spaces calls them the same thing.

Hamburger and Grimshaw in Linear Trasforms in n Dimensional Vector Space does not use the word subspce at all.

Planet Math says a Linear Manifold is a Linear Subspace possibly moved from the origin ( surely incorrect if it is a vector space ).

I assume the first source is correct, the second just uses a different name and the third is incorrect.

Is this so.

Thanks. Matheeinste