Math Notation Help

$$x>y$$  gives

$x>y$

$$x\ge~y$$ or $$x\geq~y$$ gives

$x\ge~y$

$$<$$   gives

$$x\le~y$$ or $$x\leq~y$$ gives

$x\le~y$

$$x\neq~y$$ gives

$x\neq~y$

note: \neg produces the logical negation, i.e. $$\neg~A$$ gives

$\neg~A$

• Syntax for an n-dimensional array:
  \begin{array}a₁&...&a_n\end{array}
• Ex.: $$$\begin{array}a_{\fs{0}1}\fs{3},&a_{\fs{0}2}\fs{3},&a_{\fs{0}3}\end{array}$$$ gives

$(\begin{array}a_{\fs{0}1}\fs{3},&a_{\fs{0}2}\fs{3},&a_{\fs{0}3}\end{array})$

• An (m,n)-matrix is considered as an array of m*n elements, where the elements of a column are separated by "&" and the rows by "\\".

• Syntax for an (m,n)-matrix:
  \begin{array}{colformat}a₁₁&...&a_1n\\a₂₁&...&a_2n\\... \\a_m1&...&a_mn \end{array}

  where
  colformat defines the format of each of the n columns: l for left, r for right and c for center (hence {ccccc} defines for a (m,5)-matrix in which all columns are centered)

• Ex.: $$\left(\begin{array}{lcr}a_{\tiny1}+d & a_{\tiny2}+d & a_{\tiny3}+d \\ b_{\tiny1}& b_{\tiny2}& b_{\tiny3} \\ c_{\tiny1} & c_{\tiny2} & c_{\tiny3} \end{array}\right)$$ gives

$\left(\begin{array}{lcr}a_{\tiny1}+d & a_{\tiny2}+d & a_{\tiny3}+d \\ b_{\tiny1}& b_{\tiny2}& b_{\tiny3} \\ c_{\tiny1} & c_{\tiny2} & c_{\tiny3} \end{array}\right)$

Note in the example above that "lcr" has the effect that column 1 is left aligned, column 2 centered and colums 3 right aligned.