5 Questions
What is the definition of trace in linear algebra?
The trace of a square matrix A, denoted tr(A), is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of A.
Is the trace defined for non-square matrices?
No, the trace is only defined for square matrices (n × n).
How is the trace of a matrix related to its eigenvalues?
The trace of a matrix is the sum of its (complex) eigenvalues, counted with multiplicities.
What is the property of trace for the product of two matrices?
For any two matrices A and B of appropriate sizes, tr(AB) = tr(BA).
What is the relationship between the trace and similar matrices?
Similar matrices have the same trace.
Test your knowledge of linear algebra with this quiz on matrix traces and properties. Learn about the definition of trace, its relationship to eigenvalues, and the commutative property of trace. Challenge yourself with various questions and enhance your understanding of this fundamental concept in linear algebra.
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