Business Acquisitions, Goodwill and Acquired Intangible Assets (Goodwill) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021
Goodwill [Roll Forward]
Goodwill, beginning balance	$ 2,150.0	$ 2,050.5
Current year acquisitions	5,905.5	16.9
Foreign currency changes and other	(68.8)	82.6
Goodwill, ending balance	7,986.7	2,150.0
Instrumentation
Goodwill [Roll Forward]
Goodwill, beginning balance	968.8	905.9
Current year acquisitions	0.0	16.9
Foreign currency changes and other	(32.9)	46.0
Goodwill, ending balance	935.9	968.8
Digital Imaging
Goodwill [Roll Forward]
Goodwill, beginning balance	997.8	962.7
Current year acquisitions	5,905.5	0.0
Foreign currency changes and other	(35.8)	35.1
Goodwill, ending balance	6,867.5	997.8
Aerospace and Defense Electronics
Goodwill [Roll Forward]
Goodwill, beginning balance	165.8	164.3
Current year acquisitions	0.0	0.0
Foreign currency changes and other	(0.1)	1.5
Goodwill, ending balance	165.7	165.8
Engineered Systems
Goodwill [Roll Forward]
Goodwill, beginning balance	17.6	17.6
Current year acquisitions	0.0	0.0
Foreign currency changes and other	0.0	0.0
Goodwill, ending balance	$ 17.6	$ 17.6