Jordan Normal Form — Topic Summaries
AI-powered summaries of 9 videos about Jordan Normal Form.
9 summaries
Linear Algebra 61 | Similar Matrices
Similar matrices are the algebraic way to say two matrices represent the same linear map in different coordinate systems: if there exists an...
Jordan Normal Form 1 | Overview [dark version]
Jordan normal form is the universal replacement for diagonalization: every square matrix with complex entries can be converted—via a similarity...
Jordan Normal Form 2 | An Example [dark version]
A 4×4 matrix is worked through to find its Jordan normal form, with the key takeaway that eigenvalues and their multiplicities narrow the structure...
Abstract Linear Algebra 35 | Definition of Jordan Normal Form
Jordan normal form is the canonical matrix form that every linear operator on a complex vector space can be reduced to via a change of basis, even...
Abstract Linear Algebra 38 | Invariant Subspaces
Invariant subspaces are the key structural tool behind Jordan normal form: a subspace U of a vector space V is called invariant under a linear map L...
Abstract Linear Algebra 39 | Direct Sum of Subspaces
Direct sums of subspaces are introduced as the key tool for splitting a vector space into two parts that don’t overlap except at the zero vector—and...
Abstract Linear Algebra 40 | Block Diagonalization
A linear map that respects a direct-sum decomposition of the space can always be represented by a block diagonal matrix—no mixing between the two...
Ordinary Differential Equations 23 | Example for Matrix Exponential
A 2×2 homogeneous, autonomous linear system can be solved cleanly by converting it into a matrix exponential—then making that exponential computable...
Ordinary Differential Equations 25 | Example for Non-Diagonalizable Matrix
A system of linear differential equations with a non-diagonalizable matrix still has a closed-form solution once the matrix exponential is...