---
title: Linear Operators
description: Linear operators are mappings between vector spaces that preserve vector addition and scalar multiplication. Learners will understand bounded and unbounded operators, their adjoints, and how to apply these concepts to solve differential and integral equations.
category: mathematics
subcategory: functional-analysis
difficulty: beginner, intermediate, advanced
url: /subject/linear-operators
---

# Linear Operators

Linear operators are mappings between vector spaces that preserve vector addition and scalar multiplication. Learners will understand bounded and unbounded operators, their adjoints, and how to apply these concepts to solve differential and integral equations.

## Available Resources

1 Books • 1 Courses • 1 Websites

## Courses

### 1. Introduction to Functional Analysis (MIT 18.102)

**Author:** Casey Rodriguez

Analysis on infinite-dimensional spaces: normed and Banach spaces, the Hahn-Banach theorem and duality, bounded operators, Lebesgue measure and Lp spaces, Hilbert spaces, compact and self-adjoint operators, and the spectral theorem. Includes 23 lecture videos, extensive lecture notes, problem sets and exams.

**Difficulty:** Advanced | **Price:** Free

**Link:** https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/

**Tags:** functional-analysis, banach-spaces, hilbert-spaces, spectral-theorem, operator-theory, lebesgue-integration

## Websites

### 1. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

## Books

### 1. Linear Operators in Hilbert Spaces

**Author:** Joachim Weidmann

Graduate text (Springer GTM 68) on the theory of bounded and unbounded operators in Hilbert spaces, covering self-adjoint extensions, spectral theory, and perturbation theory, with applications to differential operators from quantum mechanics. Assumes measure theory and basic functional analysis.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0387904271?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, functional-analysis

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