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  "body": "\n## Summary\n\nA Hilbert C*-module over a C*-algebra $A$ is a module over $A$ with an inner product.\nThe values of this inner product lie in $A$ instead of in $\\C$.\nIt generalizes a Hilbert space, which is the case $A = \\C$.\nHilbert modules are the basic tool of Kasparov's KK-theory and of Morita equivalence of C*-algebras.\n\n## Explanations\n\n### L1 human\n\nIn a Hilbert space the inner product of two vectors is a complex number.\nIn a Hilbert C*-module the \"numbers\" are replaced by elements of a C*-algebra, for example by continuous functions on a space.\nA typical picture is a continuous family of Hilbert spaces indexed by points of a space, with a pointwise inner product.\nThe simplest example is the algebra $A$ itself, with $\\ip{a}{b} = a^* b$.\n",
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