The solution space of is called the eigenspace of associated with the eigenvalue . The eigenspace is denoted by .
Sum/Product of Eigenvalues
– The sum of all eigenvalues of (including repeated eigenvalues) is the same as (trace of , i.e. the sum of diagonal elements of )
– The product of all eigenvalues of (including repeated eigenvalues) is the same as .
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Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students’ understanding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete Rnsetting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.