University:
University of California, Berkeley
Course:
COMPSCI 164 | Programming Languages and Compilers
Academic year:

2023
Views:

292

Pages:

11
Author:

Clint W.

The Matrix is a system, Neo. Arrays, Tables, and Multi-line Math Environments Daniel Nguyen Introduction Arrays Tables Matrices Multi-line Math XY Matrices Conclusion We can think of matrices as a subset of arrays, since they are usually declared and used as such within the wonderful world of TEX. One relevant counter-example is shown here: α β∗ A= γ∗ δ You mean it isn’t real? Arrays, Tables, and Multi-line Math Environments Daniel Nguyen Introduction Arrays Tables Matrices Multi-line Math XY Matrices Conclusion This is accomplished using the following lines of code: \begin{displaymath} A = \begin{pmatrix} \alpha & \beta^{*} \\ \gamma^{*} & \delta \end{pmatrix} \end{displaymath} An observant person will notice that this follows the same syntax as the previously mentioned array environments; the primary difference lies in the fact that pmatrix strips out the delimiters and handles the parentheses for you. What if... Arrays, Tables, and Multi-line Math Environments Daniel Nguyen Introduction Arrays Tables Matrices Multi-line Math XY Matrices Conclusion We want to print out systems of nice-looking equations, or introduce some kind of automatic cross-referencing system? Luckily, we weren’t kidding when we said LATEX could do anything you could imagine. Equation Arrays! Arrays, Tables, and Multi-line Math Environments Daniel Nguyen Introduction Arrays Tables Like the name suggests, equation arrays are arrays...of equations...more importantly, however, we know that they will use syntax similar to the cute and cuddly arrays we’ve already learned about. Here’s an example of something we’d like for our Linear Algebra homework: Matrices Multi-line Math XY Matrices Conclusion 3x1 + 5x2 − 4x3 = 0 (1) −3x1 − 2x2 + 4x3 = 0 (2) 6x1 + x2 − 8x3 = 0 (3) Ta-Da! Arrays, Tables, and Multi-line Math Environments Daniel Nguyen Introduction Arrays Tables \begin{eqnarray} 3x_{1} + 5x_{2} - 4x_{3} &=& 0 \\ -3x_{1} - 2x_{2} + 4x_{3} &=& 0 \\ 6x_{1} + x_{2} - 8x_{3} &=& 0 \end{eqnarray} Matrices Multi-line Math XY Matrices Conclusion Key things to notice here: syntax format automatic counter It should be fairly obvious that eqnarray is essentially a glorified, math-y array! Imagine Arrays, Tables, and Multi-line Math Environments Daniel Nguyen Introduction Suppose we want to suppress the automatic numbering scheme for whatever reason. It’s actually quite simple, as we demonstrate here: Arrays Tables Matrices Multi-line Math 3x1 + 5x2 − 4x3 = 0 −3x1 − 2x2 + 4x3 = 0 6x1 + x2 − 8x3 = 0 XY Matrices Conclusion Instead of declaring an eqnarray environment, all we did was use eqnarray* instead. Choices, Choices... Arrays, Tables, and Multi-line Math Environments Daniel Nguyen Introduction Who doesn’t like choices? We can also use the align environment if you don’t feel like typing out eqnarray. Arrays Tables Matrices Multi-line Math XY Matrices Conclusion 2x + 3 = 0 2x = −3 3 x =− 2 (4) (5) (6) Ezpz Arrays, Tables, and Multi-line Math Environments Daniel Nguyen Introduction Arrays Tables Matrices Multi-line Math For the lazy people out there, here’s how you would typeset the previous example: \begin{align} 2x + 3 &= 0 \\ 2x &= -3 \\ x &= -\frac{3}{2} \end{align} XY Matrices Conclusion Note the &= here, compared to the &=& from eqnarray! Like its alternative, however, you can suppress numbering by declaring the align* environment instead. One Last Thing... Arrays, Tables, and Multi-line Math Environments Daniel Nguyen Introduction Arrays Suppose you need to put together a commutative diagram for your homework. How would you do that? Here’s an example of what I’m talking about: Tables Matrices Multi-line Math XY Matrices Conclusion /B ? O ~ ~~ ~ ~ ~~ /D C A XYmatrix at Work Arrays, Tables, and Multi-line Math Environments Daniel Nguyen Introduction Arrays Tables Matrices Multi-line Math XY Matrices Conclusion This was done using the following commands: \begin{displaymath} \xymatrix{ A \ar[d]\ar[r] & B \\ C \ar[ru]\ar[r] & D \ar[u] } \end{displaymath} As you might have guessed, the syntax is similar to an array; the only real difference is that ar is used to direct the arrows. If you do end up needing to make a commutative diagram, be sure to include \input{xy} \xyoption{all} in your preamble. Conclusion Arrays, Tables, and Multi-line Math Environments Daniel Nguyen Introduction Arrays Tables Matrices Multi-line Math XY Matrices Conclusion See? Even typing math can be cool...or at least not as tedious as it could be. Remember to consult Google if you need more examples of syntax!