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<p>In this paper, we discuss possible bounds for the singular values of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(AXB^{*}\pm BYA^{*}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <mi>X</mi> <mmultiscripts> <mi>B</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mo>±</mo> <mi>B</mi> <mi>Y</mi> <mmultiscripts> <mi>A</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> </mrow> </math></EquationSource> </InlineEquation>, with brief proofs. Additionally, we extend classical results in matrix analysis by establishing new singular value inequalities for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(AX-YB\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <mi>X</mi> <mo>-</mo> <mi>Y</mi> <mi>B</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\Re AX^{*}B^{*}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ℜ</mi> <mi>A</mi> <mmultiscripts> <mi>X</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mmultiscripts> <mi>B</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Singular value inequalities involving positive semidefinite matrices

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Hefang Jing,
  • Feng Zhang

摘要

In this paper, we discuss possible bounds for the singular values of \(AXB^{*}\pm BYA^{*}\) A X B ∗ ± B Y A ∗ , with brief proofs. Additionally, we extend classical results in matrix analysis by establishing new singular value inequalities for \(AX-YB\) A X - Y B and \(\Re AX^{*}B^{*}\) ℜ A X ∗ B ∗ .