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Goodwill and Other Intangible Assets - Narrative (Details) - USD ($)	3 Months Ended				6 Months Ended		12 Months Ended
	Jul. 02, 2021	Apr. 02, 2021	Jul. 03, 2020	Apr. 03, 2020	Jul. 02, 2021	Jul. 03, 2020	Jan. 01, 2021
Finite-Lived Intangible Assets [Line Items]
Non-cash goodwill impairment charge					$ 62,000,000	$ 369,000,000
Amortization expense for intangible assets	$ 156,000,000		$ 209,000,000		320,000,000	367,000,000
Aviation Systems
Finite-Lived Intangible Assets [Line Items]
Non-cash goodwill impairment charge					62,000,000	364,000,000
Commercial Aviation Solutions | COVID-19
Finite-Lived Intangible Assets [Line Items]
Non-cash goodwill impairment charge			54,000,000	$ 296,000,000
Non-cash goodwill impairment charge attributable to noncontrolling interests			8,000,000	$ 28,000,000
CTS
Finite-Lived Intangible Assets [Line Items]
Non-cash goodwill impairment charge					0
Non-cash impairment charge of asset group	56,000,000				56,000,000
Non-cash impairment charge of intangible assets	7,000,000				7,000,000
CTS | Aviation Systems
Finite-Lived Intangible Assets [Line Items]
Non-cash impairment charge of asset group	145,000,000
Non-cash impairment charge of intangible assets	63,000,000
Held-for-sale
Finite-Lived Intangible Assets [Line Items]
Goodwill assigned to disposal group	26,000,000				26,000,000
CPS business | Disposed of by Sale | Aviation Systems
Finite-Lived Intangible Assets [Line Items]
Goodwill assigned to disposal group		$ 174,000,000
CPS business | Held-for-sale | Aviation Systems
Finite-Lived Intangible Assets [Line Items]
Non-cash goodwill impairment charge		$ 62,000,000
VSE disposal group | Held-for-sale
Finite-Lived Intangible Assets [Line Items]
Goodwill assigned to disposal group	$ 0		14,000,000		$ 0	14,000,000
VSE disposal group | Held-for-sale | Aviation Systems
Finite-Lived Intangible Assets [Line Items]
Goodwill assigned to disposal group			14,000,000			$ 14,000,000
Non-cash goodwill impairment charge			$ 14,000,000				$ 14,000,000

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