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In my course, one defines $B_{n, d}(x)$ as “a basis of monomials of degree at most $d$.”

I also have an example for $n=1$ :

$$ B_{1, 2}(x) = \begin{pmatrix} 1\\ x\\ x^2 \end{pmatrix} $$

But I cannot find an example online of such a basis of monomials for more than 1 variable. For instance, what would $B_{2, 2}(x)$ be ? My guess would be something like

$$ B_{2, 2}(x) = \begin{pmatrix} 1 & 1\\ x_1 & x_2^2\\ x_1^2 & x_2^2 \end{pmatrix} $$

But I am really not sure.

Pooyanoss
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1 Answers1

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A basis $\;B_{2,2}(x)\;$ is the following one :

$$ B_{2, 2}(x) = \begin{pmatrix} 1\\ x_1\\ x_2\\ x_1x_2\\ x_1^2\\ x_2^2 \end{pmatrix} $$

Angelo
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