Questions askedCategory: 2568Chapter 3.3 Examples of Subspaces

Dear Dr. Tsumura,
If we are ask to determine W = Sp{ vector u, vector v} given vector u and v, could I apply
W = column space of Sp
= row space of Sp^Transpose ?
Hope to hear back from you soon. Thank you.

Yu Staff answered 10 months ago

First of all, the column space of $\Span$ does not make sense. We defined the column space of a matrix.
So before talking about the column space, you need to define a matrix $A=[\mathbf{u}, \mathbf{v}]$.
Then you can say $W$ is the column space of $A$. (Or the row space of $A^{\trans}$.)
If you want to find a basis of $W$, then you can use the leading 1 method.

Ok. Noted. Thank you, Dr. Tsumura.