Suppose \(v \in V\), and \(U \subset V\). Then, \(v+U\) is the subset (not a subspace, obviously):

\begin{equation} v + U = \{v+u : u \in U\} \end{equation}

A function \(T: V\to W\) is surjective if its range equals its codomain \(W\). “onto”

“For any possible output, \(w \in W\) for \(T \in \mathcal{L}(V,W)\), there is at LEAST one input \(T\) that maps \(Tv \to w\). "

\begin{equation} \forall w \in W, \exists v \in V:Tv=W \end{equation}

map to bigger space is not surjective

See map to bigger space is not surjective

syscalls are public functions that allow user land operations to access system-level services (such as reading a sector) which otherwise is locked in kernel mode because they require special privileges.

These functions are called completely isolated to another function: 1) private stack frame 2) private memory, etc.

open, close, read, write

kernel mode

kernel mode allows superuser function access such as reading sectors, etc. which would be dangerous if public.

file

open

int open(const char *pathname, int flags, mode_t mode);

Flags are a bitwise OR operations: you have to open with O_RDONLY (read only), O_WRONLY (write only), or O_RDWR (both read and write). This returns \(-1\) if the reading fails.