Скачать или смотреть Finding Eigenvalues of a 3x3 Matrix | Easy to Follow with Step-by-Step Example

Learn how to EASILY find the eigenvalues of a 3×3 Matrix – Step by Step! In this video, I break down what eigenvalues are and show you exactly how to calculate them for a 3×3 matrix using a structured, easy-to-follow method.

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Key Moments
00:18 Eigenvalue Definition
02:36 Example - Finding the Eigenvalues of a 3x3 matrix
05:01 Laplace Expansion to find the determinant
10:25 Factoring the cubic polynomial (characteristic equation) to find the eigenvalues (roots)
13:35 Synthetic Division
17:18 Jump to the Solution (found the eigenvalues)

💡 What Are Eigenvalues?
Eigenvalues are special scalars associated with a square matrix that describe how the matrix stretches or compresses space when applied to a vector. If A is a square matrix and v is a nonzero vector, then the eigenvalue λ satisfies the equation: 𝐴𝑣 = 𝜆𝑣

💡 How to Find Eigenvalues of a 3×3 Matrix:
1️⃣ Start with the characteristic equation → Find det(A - λI) = 0
2️⃣ Expand the determinant → Solve for λ by finding the roots of the characteristic polynomial
3️⃣ Get the eigenvalues → The solutions to the polynomial equation give you the eigenvalues of the matrix

📌 Key Facts About Eigenvalues:
✔️ The number of eigenvalues is equal to the size of the square matrix (a 3×3 matrix has 3 eigenvalues)
✔️ Some eigenvalues can be repeated (multiplicity) or even complex numbers
✔️ Eigenvalues are used in machine learning, physics, engineering, and differential equations
✔️ Applications include principal component analysis (PCA), dimensionality reduction, quantum mechanics, and Markov chains

📢 Perfect for:
✔️ Linear Algebra Students
✔️ Data Science & Machine Learning Enthusiasts
✔️ Engineering & Physics Students
✔️ AI & Deep Learning Practitioners
✔️ Anyone preparing for exams like SAT, GRE, or university-level math courses

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This video is a math lecture in linear algebra, eigenvalues, eigenvectors, matrices and machine learning as part of my math series about Linear Algebra. Subscribe to my channel if you want to learn more about math and cool math tricks!

Key Moments
00:18 Eigenvalue Definition
02:36 Example - Finding the Eigenvalues of a 3x3 matrix
05:01 Laplace Expansion to find the determinant
10:25 Factoring the cubic polynomial (characteristic equation) to find the eigenvalues (roots)
13:35 Synthetic Division
17:18 Jump to the Solution (found the eigenvalues)

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