Linear Algebra 4g: A Good Way to Express Linear Subspaces in ℝⁿ

[xoppa]

"determine if the target vector is in the span of the decomposition vectors"
I like that description!! This relates perfectly to solving matrix equations Ax = b. Specifically Ax = b has a solution if b is in the subspace spanned by the column vectors of A. Here b is the "target vector", and the column vectors of A are the decomposition vectors.

[acruzp]

In the second example, the one with a zero directly inside the vector expression, it's better to use greek letters to avoid confusion with the letter O, even though it is avoided precisely because of this.

[michaellewis]

Why not use a psuedo set theoretical notation.
{[a b c]| a, c£R, b=0}