---
title: "Scalars, vectors, matrices, and tensors"
description: "Classify numerical objects by their axes and the roles those axes play."
canonical_url: "https://fanout.sh/ml-math/decoder/scalars-vectors-matrices-and-tensors"
md_url: "https://fanout.sh/ml-math/decoder/scalars-vectors-matrices-and-tensors.md"
last_updated: "2026-08-09"
access: "public"
---

# Scalars, vectors, matrices, and tensors

Classify numerical objects by their axes and the roles those axes play.

## Public overview

How many axes does this object have, and what does each axis mean?

Assign a provisional mathematical type to each important object.

Check whether the operation is valid for the stated types and shapes.

Use a type or shape mismatch to locate a reading error.

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