The numerical range of 3 × 3 matrices Original Research Article

Let A be an n × n complex matrix. Then the numerical range of A, W(A), is defined to be {x*Ax: x set membership, variant Cn, x*x = 1}. In this article a series of tests is given, allowing one to determine the shape of W(A) for 3 × 3 matrices. Reconstruction of A, up to unitary similarity, from W(A) is also examined.