Space of Polynomials over a Field form a Vector Subspace of Function Vector Space

Statement Let $F$ be a and denote $$P[F] = \{x \mapsto \sum\limits{k=0}^{n} c{k}x^{k} : n \in \mathbb{Z}{\geq 0}; c{0}, \dots,...

11/7/2022

Infinite-Dimensional Vector Space

Definition Let $V$ be a . We say that $V$ is an if it is not a . Remarks Note that this...

11/7/2022

Univariate Polynomials on Real Numbers are Infinite-Dimensional

Statement Let $P[\mathbb{R}]$ be the space of polynomial over $\mathbb{R}$. $P[\mathbb{R}]$ is an . Proof - Use and ....

11/7/2022

Dimension of Subspace cannot be bigger than Parent Vector Space

Statement Let $V$ be a and let $W \subset V$ be a of $V$. Then $\dim W \leq \dim...

11/7/2022