The Matrix was a nightclub in San Francisco from 1965 to 1972 and was one of the keys to what eventually became known as the "San Francisco sound" in rock music. Located at 3138 Fillmore Street in Cow Hollow, in a 100-capacity beer-and-pizza shop, The Matrix opened 13 August 1965, showcasing Jefferson Airplane, which singer Marty Balin had put together as the club's "house band". Balin had persuaded three limited partners to put up $3,000 apiece to finance the club's opening, giving them 75 percent ownership, while he retained 25 percent for creating and managing it.

Jefferson Airplane rose rapidly to local prominence during late 1965 and early 1966 with their performances at The Matrix, and it was there that they were first seen by noted music critic Ralph J. Gleason, who became an early champion of the group.

The Matrix was a favorite haunt of gonzo journalist Hunter S. Thompson in the late 1960s – it was briefly mentioned in Fear and Loathing in Las Vegas during a flashback. Thompson was a contributing editor for Rolling Stone magazine (founded in 1967 in San Francisco).

The Matrix was an important venue in the formative years of the San Francisco rock music scene, featuring not only rock bands but also several blues artists and blues bands, with an occasional jazz artist thrown in. Besides Jefferson Airplane, many other well-known bands and musicians performed there:

Created and operated by musicians, the Matrix was popular with local and visiting musicians. On their off nights, many would go there to hear other groups they knew or just to visit. Management would waive the cover charge for prominent musicians who entered the club as customers.

In the early years of The Matrix, there was a huge mural of the Four Horsemen of the Apocalypse on the left wall near the rear; rumor was that the members of Jefferson Airplane had painted it before the club first opened. Another wall was adorned with hieroglyphics. The club's lighting was very subdued everywhere but on its small stage.

The club itself was very small; its max occupancy was only around 120 people. The entrance was recessed about two feet and was left of center on the windowless wall seen from the street, and there was a cabinet outside to the door's right where upcoming bands were listed and handbills were posted. Inside, near the entrance, there was a bar (beer and wine license only) on the front left. The interior was about 50 by 80 feet. The ceiling at the front third of the club was about ten feet high, but farther back, it went up to about 18 feet. The right front area had chairs and most of the cocktail tables, while the center of the room to the rear was a dance floor. The stage was a step above the floor on the right side, center to rear. A small sound booth occupied the center of the left wall, and a few cocktail tables were at the left rear in front of the mural. The rear wall had a window opening for the small galley used to prepare food.

Sometime in 1966 or 1967, Marty Balin sold his share of the club to Peter Abram and Gary Jackson, two of the original partners; they bought out the remaining partner. Abram actively managed the club room and made bookings while also recording those musicians he knew and liked. Jackson took care of accounting and general business matters. For a brief period toward the end of 1966, Bill Ehlert, better known as the "Jolly Blue Giant" or simply "Jolly", owner of the Jabberwock in Berkeley, took over running The Matrix. This brought a distinct change to the booking policy whereby Jabberwock favorites Country Joe and the Fish, the New Age and Blackburn & Snow performed. Another change was seen in the advertising of shows, with Jabberwock house artist Tom Weller producing some classic posters and handbills.