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