Characteristic Polynomial — Topic Summaries
AI-powered summaries of 11 videos about Characteristic Polynomial.
11 summaries
A quick trick for computing eigenvalues | Chapter 15, Essence of linear algebra
For 2×2 matrices, eigenvalues can be computed almost instantly by reading two numbers off the matrix—its trace and determinant—then using a...
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...
Linear Algebra 59 | Adjoint
Adjoint matrices are introduced as the complex-number counterpart to the transpose, and they’re pinned down by how they interact with the inner...
Linear Algebra 54 | Characteristic Polynomial
Eigenvalues can be found by turning a matrix problem into a single-variable polynomial: the characteristic polynomial. For a square matrix A, an...
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...
Linear Algebra 63 | Spectral Mapping Theorem
The spectral mapping theorem for polynomials gives a direct rule for how eigenvalues change when a matrix is transformed by a polynomial: the...
Linear Algebra 55 | Algebraic Multiplicity
Algebraic multiplicity measures how many times a particular eigenvalue shows up as a repeated root of the characteristic polynomial, and that...
Ordinary Differential Equations 24 | Characteristic Polynomial
For linear, homogeneous, autonomous differential equations of order n, the path to the general solution runs through the characteristic...
Linear Algebra 54 | Characteristic Polynomial [dark version]
Eigenvalues can be found by turning a matrix problem into a single polynomial equation: for a square matrix A, the eigenvalues are exactly the zeros...
Linear Algebra 59 | Adjoint [dark version]
Adjoint matrices are the complex-matrix counterpart of transposes, and they’re built to make the inner product work correctly in n. In real vector...
Linear Algebra 55 | Algebraic Multiplicity [dark version]
Algebraic multiplicity measures how many times a given eigenvalue shows up as a repeated root of the characteristic polynomial—so it’s the “counting...