第一步是解特徵方程式找到特徵值，第二步是根據特徵值找到對應的特徵向量。
給定一個 的方矩陣 ，若存在一個非零向量 以及一個常數 ，滿足以下公式
透過對 乘上 單位矩陣，得到 ，使純量成為特徵矩陣，再透過矩陣乘法的分配律，使合併，得到
只有在 時才會有多個非零解。
這是一個以 為變數的多項式方程式，其階數最多為矩陣 的階數 ， 的可能解最多有 個
代入每個 ，解該線性系統，找出非零解 。
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Note content emphasizes mathematics used in computer science and AI fields, organizing concept, symbol, and formula key contexts as quick reference, learning route planning, and direct application lookup. Used for marking element or item positions. Finite index interval addition operations. Finite index interval multiplication operations. Basic relationship of element belonging to sets.
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Note content emphasizes mathematics applied in computer science and AI fields, providing quick reference of key contexts and formulas similar to mind maps, helping learning route planning or direct formula lookup. Matrix notation, vector definitions, matrix operations, determinants, eigenvalues and eigenvectors, and other fundamental linear algebra concepts.
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Note content emphasizes mathematics used in computer science and AI, organizing concept, symbol, and formula key contexts as quick reference for learning routes and application lookup. Sequences arrange elements by index; series sum sequence terms. For finite series, partial sums can be considered; for infinite series, convergence depends on partial sum sequence limits. Geometric series have first term a and common ratio r, with specific sum formulas.
