LinkedIn personal banners: 1584×396 pixels, 4:1, JPG or PNG, up to 8MB. Company pages use 1512×256; the 1128×191 figure in older guides is out of date. Drop an image; it returns at exactly 1584×396, ready to upload without LinkedIn's own cropper mangling it.
The rule that matters most concerns the bottom left. The profile photo overlays roughly a 568×264 region there on desktop and mobile alike, and anything placed behind it simply disappears. Compose to the right two-thirds or dead centre; the crop position slider shifts the source to clear the overlap.
Fitting photos to 4:1: the ratio is very wide, and most images lose significant top and bottom. Landscape sources with the subject placed high survive best; wide scenes, textures and skylines take the trim gracefully; group shots mostly don't.
Text in banners wants to be large and right of centre, because on phones the banner renders around 200 pixels tall, which is not enough height for small lettering to stay legible.
JPG encoding and the 8MB ceiling are handled automatically, and each file reports what it weighs. At 4:1 the banner is a wide, shallow strip. A busy photograph rarely holds up in it, while flat colour with a single focal point holds up far better than detail nobody can pick out.