# Lists, Factors and Matrices — R Programming

Source: https://www.geekswithgeeks.com/en/r-programming/d-lists

> Use lists for mixed data, factors for categories and matrices for 2D numeric data.

## Beyond simple vectors

A **list** holds elements of **different types and lengths**, including other lists, making it R's general-purpose container: results of a model, a parsed JSON document, or a record about a customer. Access elements with **`[[ ]]`** or **`$`** (`order$items`), while single brackets `[ ]` return a **sub-list**. A **factor** represents **categorical data** with a fixed set of **levels**, stored as integers with labels; factors control the order of categories in plots and models, and **ordered factors** support comparisons such as `"low" < "high"`. The **forcats** package helps reorder, lump and relabel levels. A **matrix** is a two-dimensional atomic vector (all one type) with rows and columns, indexed as `m[row, col]`, and supports matrix algebra (`%*%` for multiplication, `t()` for transpose, `solve()` for inverses); **arrays** generalise to more dimensions. Use `str()` to inspect the structure of any object quickly.

## Lists, factors and a matrix

[[ ]] extracts an element; [ ] returns a smaller list.

```r
order <- list(
  id = "o-1001",
  customer = "Asha",
  items = c("pen", "notebook"),
  totals = list(subtotal = 169.5, gst = 30.51)
)

order$items                    # character vector
order[["totals"]]$gst          # nested access
order["id"]                    # a list containing id
str(order)                     # compact structure overview

sizes <- factor(c("M", "S", "L", "M"), levels = c("S", "M", "L"), ordered = TRUE)
levels(sizes)                  # "S" "M" "L"
table(sizes)                   # counts in level order
sizes[1] < sizes[3]            # TRUE: M < L

sales <- matrix(c(10, 12, 8, 15, 9, 11), nrow = 2, byrow = TRUE,
                dimnames = list(c("Pune", "Delhi"), c("Jan", "Feb", "Mar")))
sales["Delhi", "Feb"]          # 9
rowSums(sales)                 # Pune 30, Delhi 35
```

## A folder versus the paper inside

A list is a folder. `order["items"]` hands you a smaller folder containing the items page; `order[["items"]]` takes the page itself out of the folder.

**Quiz:** For a list x, what is the difference between x["a"] and x[["a"]]?

- [ ] There is none
- [x] x["a"] returns a sub-list; x[["a"]] returns the element itself
- [ ] x[["a"]] returns a sub-list
- [ ] Both throw errors

*Answer:* x["a"] returns a sub-list; x[["a"]] returns the element itself. Single brackets keep the list container; double brackets extract the content.