MathDB
Problem 10 IMC 2004 Macedonia

Source:

July 26, 2004
linear algebramatrixalgebrapolynomialvectorIMCcollege contests

Problem Statement

For n≥1n\geq 1 let MM be an n×nn\times n complex array with distinct eigenvalues λ1,λ2,…,λk\lambda_1,\lambda_2,\ldots,\lambda_k, with multiplicities m1,m2,…,mkm_1,m_2,\ldots,m_k respectively. Consider the linear operator LML_M defined by LMX=MX+XMTL_MX=MX+XM^T, for any complex n×nn\times n array XX. Find its eigenvalues and their multiplicities. (MTM^T denotes the transpose matrix of MM).
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