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Goodwill and Other Intangible Assets, Intangible Assets (Details) - USD ($) $ in Millions | 3 Months Ended |
--- | --- | ---
Mar. 31, 2021 | Dec. 31, 2020
Intangible Assets |  |
Weighted average useful lives of acquired amortizable intangible assets | 9 years |
Gross Carrying Amount (definite-lived) | $ 685.6 | $ 662.5
Accumulated Amortization | 461.4 | 451.1
Net Carrying Amount, (definite-lived) | 224.2 | 211.4
Indefinite-lived trade name intangible asset | 186.1 | 186.1
Intangible assets, gross (excluding goodwill) | 871.7 | 848.6
Net Carrying Amount, intangible assets | $ 410.3 | 397.5
Customer relationships |  |
Intangible Assets |  |
Weighted average useful lives of acquired amortizable intangible assets | 9 years |
Gross Carrying Amount (definite-lived) | $ 479.9 | 456.6
Accumulated Amortization | 321.1 | 313.6
Net Carrying Amount, (definite-lived) | $ 158.8 | 143.0
Proprietary technology |  |
Intangible Assets |  |
Weighted average useful lives of acquired amortizable intangible assets | 11 years |
Gross Carrying Amount (definite-lived) | $ 156.0 | 156.2
Accumulated Amortization | 90.9 | 88.1
Net Carrying Amount, (definite-lived) | $ 65.1 | 68.1
Backlog and other |  |
Intangible Assets |  |
Weighted average useful lives of acquired amortizable intangible assets | 2 years |
Gross Carrying Amount (definite-lived) | $ 49.7 | 49.7
Accumulated Amortization | 49.4 | 49.4
Net Carrying Amount, (definite-lived) | $ 0.3 | $ 0.3

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