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A subspace is a vector space which is a subset of a vector space, using the same addition and scalar multiplication operations. Intuitively, a subspace of \(\mathbb{R}^{2}\) are all the lines through the origin as well as \(\{0\}\); a subspace of \(\mathbb{R}^{3}\) are all the planes through the origin as well as \(\{0\}\), etc. etc.

constituents

• vector space \(V\)
• A subset \(U \subset V\) which is itself a vector space

requirements

You check if \(U\) is a subspace of \(V\) by checking IFF the following three conditions:

the pocket at which the ligand binds to the enzyme

The sum of subsets is the definition of addition upon two subsets.

Apparently, the unions of subsets are almost never subspaces (they don’t produce linearity?) Therefore, we like to work with sum of subsets more.

Remember this has arbitrarily many things!! as a part of the content. When defining, remember to open that possibility.

constituents

Sub-sets of \(V\) named \(U_1, U_2, \dots, U_{m}\)

requirements

The sum of subsets \(U_1, \dots, U_{m}\) is defined as:

\begin{equation} U_1, \dots, U_{m} = \{u_1+\dots+u_{m}: u_1\in U_1, \dots, u_{m} \in U_{m}\} \end{equation}

Consider “what’s the variable representing the sum of the result of 2 dice?”

\begin{equation} Y = \sum_{i=1}^{2} X \end{equation}

where \(X\) is a random variable representing the result of once dice.