It can be seen that this is a linear transformation that rotates around the blue point, and as the author of the article, I can tell you exactly that all the points are rotated by radians (the blue point, the center point, can also be considered to be rotated by radians). Λ n ( a 11 a 22 ⋯ a n n ) λ n − 1 a 11 a 22 ⋯ a n n ⋯ = 0 \lambda^n (a_ x Convenient for observation): After unfolding, you can get the following form: Its essence is also a λ λ λIt is an equation of degree n in one unknown. The relationship between roots and coefficients of a quadratic equation in one variableįirst look at the quadratic equation of one variable. I have been using the sum of the trace equal to the eigenvalue to find the eigenvalue, but I have never thought about how the two are connected. Leaving this point, I feel that the trail has lost its foothold. Because the characteristic value is so important, the trace is defined. The most fundamental thing is that the sum of the trace and the characteristic value is equal. The trace of the matrix represents the sum of all the elements of the main diagonal of the matrix A AA
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