# Scalars, vectors, matrices & tensors > A thermostat reading, a drone's position, a thermal camera, and a phone video—all numbers arranged in different ways. Type: lesson Canonical: https://nithinraphael.com/learn/machine-learning/scalars-vectors-matrices-tensors Parent: machine-learning Status: published --- # Scalars, vectors, matrices & tensors A thermostat reading. A drone’s position. A thermal camera. A phone photo. They seem completely different in the real world—but underneath, they’re all **numbers organized in different ways**. As the information becomes more complex, we need more ways to organize those numbers. That takes us from **scalar → vector → matrix → tensor**. *** ## Scalar Sometimes, **one number is enough**. A room temperature of `22°C` can be described completely with a single value. That makes it a **scalar**. Scalars appear everywhere: speed, distance, price, battery percentage, temperature, and many other measurements can all be represented by one number. > Interactive component: Scalar Interactive. No matter where you move the slider, the room temperature is still described by **one value**. `22°C` → **Scalar** A scalar answers a simple question: **How much?** But one number stops being enough when we need to describe something like a position. *** ## Vector Imagine telling a delivery drone where to go. One number cannot describe its position on a flat map. The drone needs both a **horizontal position** and a **vertical position**. We can store those values together: `[x, y]` That ordered list of values is a **vector**. For example: `[6, 3]` could mean 6 units across and 3 units up. > Interactive component: Vector Interactive. Move horizontally and one value changes. Move vertically and another value changes. Together, the numbers describe **one position**. The order matters. `[6, 3]` and `[3, 6]` point to different locations because each value has a different role. Vectors are useful for more than positions. They can represent things like: - velocity: `[vx, vy]` - GPS-style coordinates: `[latitude, longitude]` - a pixel’s color: `[red, green, blue]` - a point in 3D space: `[x, y, z]` A vector gives us several related values arranged along **one axis**. What if we need many values arranged both across and down? That gives us a matrix. *** ## Matrix A thermal camera does not measure just one point. It measures temperatures across an entire area, producing values arranged in **rows and columns**. For example: ```text 21 22 24 25 20 23 29 31 19 22 27 28 ``` This two-dimensional grid of numbers is a **matrix**. A matrix has two axes: `rows × columns` Each value has a location determined by both its row and its column. > Interactive component: Matrix Interactive. The temperature itself is still a scalar. But the complete thermal scan contains many temperatures arranged across two axes, so the entire dataset is a **matrix**. Matrices show up in many familiar places: - spreadsheets - grayscale images - game maps - seating charts - sensor grids - scientific measurements A grayscale image, for example, can be stored as a matrix where every number represents the brightness of one pixel. So a matrix handles rows and columns well. But a color photo needs something extra. *** ## Tensor A phone photo may look like one flat image, but the computer stores much more underneath. Each pixel usually contains separate **red, green, and blue values**. That means we can think of the image as three grids stacked together: - one red layer - one green layer - one blue layer Now the data has three axes: `height × width × channels` This multi-axis collection of values is a **tensor**. > Interactive component: Tensor Interactive. Each individual color layer is matrix-like. Stack the three matrices together and you add another axis: **color channel**. For example: `1080 × 1920 × 3` could describe an image that is: - 1080 pixels high - 1920 pixels wide - 3 color channels Tensors can have even more axes. A video adds time: `time × height × width × channels` A machine-learning model processing several images at once might use: `batch × height × width × channels` This is why tensors are so common in **machine learning and deep learning**. Images, video, audio, and other complex datasets often need several axes to organize all their values. The word *tensor* may sound advanced, but the basic idea is straightforward: **more axes, same basic ingredient: numbers.** *** ## The pattern The easiest way to remember the progression is to focus on how the values are organized. - **Scalar** — one value - **Vector** — values along one axis - **Matrix** — values across two axes - **Tensor** — values organized across additional axes Think of it as adding structure: `22°C` **Scalar:** one value `[6, 3]` **Vector:** an ordered list ```text 21 22 24 20 23 29 19 22 27 ``` **Matrix:** rows and columns `height × width × channels` **Tensor:** multiple axes The numbers themselves are still ordinary numbers. We have simply added more ways to organize them. A useful question to ask whenever you encounter a new dataset is: **How many axes do I need to organize the values?** That question can often tell you which structure you are looking at. *** > Interactive component: Matching Quiz.