Hematite is iron oxide, and it is named for blood: the Greek haima, by way of the property that identifies it in the field.
A hematite specimen may be black, steel grey, brick red or a bright metallic silver, and none of that is reliable. What is reliable is the streak. Drawn across an unglazed porcelain plate, hematite always leaves a red-brown line, whatever the colour of the lump, because the powder is red even when the mass is not. That test is centuries old, it costs nothing, and it separates hematite from magnetite and from most other dark oxides immediately.
The same red powder is the pigment discussed elsewhere in this atlas as red ochre. Hematite and ochre are the same substance at different grain sizes and purities, which links the polished mirror-like specular hematite of a Bronze Age burial to the earth used on the walls of a painted cave.
Polished hematite was worked into mirrors in Anatolia and in Mesoamerica, where flat and concave hematite mirrors are known from Olmec contexts onward, and it was used for seals and for small carvings across the ancient Near East. It is heavy, it takes a mirror polish, and it is hard enough to hold an edge on an engraving.
One modern caution belongs here. The heavy black magnetic material sold as magnetic hematite or hematine is not hematite at all: it is a manufactured barium or strontium ferrite. Natural hematite is at most weakly attracted to a magnet.