Jordan Canonical Form for a 2x2 Matrix with Repeated Eigenvalue (& 1 Linearly Independent E-vector) скачать в хорошем качестве

Jordan Canonical Form for a 2x2 Matrix with Repeated Eigenvalue (& 1 Linearly Independent E-vector)

The 2x2 matrix A=[-5 1][-1 -3] has a repeated eigenvalue and only one linearly independent eigenvector. It is therefore not diagonalizable. But, we can still find an invertible matrix P so that J=P^(-1)AP is the Jordan canonical form (a.k.a. Jordan normal form) for A, which is upper triangular with a "1" in the upper right spot and the eigenvalue repeated along the main diagonal. In particular, if P=[1 0][1 1], then J=P^(-1)AP=[-4 1][0 -4]. This is useful for solving the linear system dY/dt=AY using the coordinate change and the matrix exponential. Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter:   / billkinneymath   🔴 Follow me on Instagram:   / billkinneymath   🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ 🔴 Desiring God website: https://www.desiringgod.org/ AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.