5.特征值和特征向量

image-20250928180417184

定义

image-20250928180541594

求法

image-20250928180716114

image-20250928180906389

image-20250928181035585

image-20250928181056142

image-20250928181125252

重要性质和结论

特征值

image-20250928181349536

image-20250928181512153

特征向量

image-20250928181549437

image-20250928181605590

image-20250928181618269

image-20250928193136860

image-20250928193253303

image-20250928203506927

image-20250928203515672

image-20250928203608087

image-20250928203752736

image-20250928203806115

矩阵的相似

定义

image-20250928203906708

性质

image-20250928203927749

image-20250928204058646

重要结论

image-20250928205500593

image-20250928205523897

image-20250928205602263

判别与证明

image-20250928212109350

矩阵的相似对角化

image-20250928212554015

image-20250928212645130

image-20250928212754832

image-20250928212822079

image-20250928212837481

image-20250928212920485

image-20250928213012366

image-20250928213225002

image-20250928213326149

image-20250928213658913

image-20250928213707479

image-20250928213753690image-20250928213801734

image-20250928213849624

image-20250928213902187

实对称矩阵的相似对角化

image-20250928214015242

image-20250928214140576

image-20250928214230111

image-20250928214321022

image-20250928214450427

image-20250928214512188