# Halcyon Calc - Working With Arrays

Halcyon Calc can manipulate matrices and vectors. Collectively, matrices and vectors are referred to as "arrays" in Halcyon Calc. A vector is "N" real or complex numbers making up a one dimensional array of values. A matrix is "N" x "M" real or complex numbers making a two dimensional array of values.

# Entering Vectors and Matrices:

Because vectors and matrices are a collection of one or more real or complex numbers, it is worth reviewing how to enter real numbers and how to enter complex numbers. A real vector can be entered like this:

```[A B C]
```

where A, B and C are entered just like real numbers. This creates a vector with three values. A vector must have at least one value and can have many more than three. Note that you can use a comma (or a period of the radix character is set to comma) to separate values instead of space. Also, the closing square bracket is not required if this is the last value being entered.

Similarly, a complex vector can be entered like this:

```[(A,B) (C,D) (E,F)]
```

where A, B, C, D, E and F are entered just like real numbers. This creates a complex vector of three values but you can create vectors with more or fewer items. As above, comma can be used as a separator and the final square bracket is optional if this is the end of the line. In fact, the final round bracket can be left off if "F" is at the end of the line. You can mix pure real numbers and complex numbers when entering a vector. When parsed by the calculator, if there is at least one complex value in the vector, the entire vector will appear as complex values.

A real matrix can be entered like this:

```[[A B C][D E F]]
```

where A, B, C, D, E and F are entered just like real numbers. This creates a real matrix with two rows and three columns. You can use commas instead of spaces to separate between values. Also, the closing square brackets are optional. So, this can be entered as:

```[[A B C[D E F
```

A complex matrix can be entered like this:

```[[(A,B) (C,D) (E,F)][(G,H) (I,J) (K,L)]]
```

where A through L are entered as real numbers. This creates a complex matrix with two rows and three columns. As before, commas can be used instead of spaces between items. The closing square brackets and even the final closing bracket is optional:

```[[(A,B) (C,D) (E,F)[(G,H) (I,J) (K,L
```

# Formatting Vectors and Matrices:

Because vectors and matrices are made up of several real or complex values, they can be very long and difficult to read. However, if you don't all digits of precision in the output, you may want to change number formatting to make the display more readable. Formatting real numbers describes how to do this. When you switch formatting modes, real numbers, complex numbers, vectors and matrices on the stack will automatically be displayed in the new formatting mode.

# Manipulating Vectors and Matrices:

There are many operations which you can use when working with vectors and matrices. The standard addition, subtraction, multiplication and division operations work but so do many other operations. Here are some links to reference material which are relevant for complex numbers: