Worked Examples

Browse common examples from different branches of math, each written with clear step-by-step instructions.

Showing 2 worked examples in Linear Algebra.

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All Subjects Calculus (8)Differential Equations (1)Linear Algebra (2)Numerical Methods (1)

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Diagonalize a $2 \times 2$ matrix and compute $A^{n}$

Diagonalization is one of the first places students see why eigenvalues matter computationally. Once $A = P D P^{- 1}$ , powers of $A$ become powers of a diagonal matrix.

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Worked ExampleLinear AlgebraEigenvalue & Eigenvector Calculator

Compute eigenvalues and eigenvectors of a $3 \times 3$ matrix

A first serious 3 by 3 eigenproblem should show new structure without burying the point in arithmetic. This one does that: you see the characteristic polynomial, the eigenspaces, and the diagonalization test in one pass.

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Worked Examples

Diagonalize a 2×2 matrix and compute An

Compute eigenvalues and eigenvectors of a 3×3 matrix

Diagonalize a $2 \times 2$ matrix and compute $A^{n}$

Compute eigenvalues and eigenvectors of a $3 \times 3$ matrix