Matrix is best known as the club originally backed by Jefferson Airplane vocalist Marty Balin, and through the 1960s it was the local venue for all the Fillmore bands on their way up or their night off. Located at 3138 Fillmore Street, in the Marina District, it was an essential part of San Francisco rock history. There was also a little known second incarnation of The Matrix, however, at 412 Broadway.
The first Matrix closed in early 1971. Original Matrix owner/operator Peter Abram (along with John Barsotti and Dave Martin) re-opened the club at a new site in late Summer 1973 . Although the second Matrix was not really a success, there were a number of good shows there in the second half of 1973. The New York Dolls played there in September (Sep 4-6), and the then-unknown Bob Marley and The Wailers played some legendary gigs there in October (Oct 19-20, 29-30).
In retrospect, an equally legendary gig has to have been the Halloween 1973 show featuring Iggy and The Stooges and The Tubes. The ad (from the Fremont Argus of October 26, 1973) says "Halloween Party with Iggy and The Stooges, The Tubes and Sugardaddy." Iggy Stooge--as he was known in those days--was a notorious engine of destruction. His new album Raw Power featured original Stooges Scott Asheton on drums and Ron Asheton (on bass), along with new guitarist James Williamson (whose presence nudged Ron Asheton over to bass). Iggy's stage act typically featured frenzied madness and self-mutilation. If I remember correctly--I cannot find the direct reference--Joel Selvin's review (he was the SF Chronicle rock critic) could barely describe the lunacy of Iggy's show, including a young lady in the audience performing a certain act (which wasn't described). Iggy soon ended up in the Hospital.
The Tubes would become one of San Francisco's rock legends within 18 months, but at the time they were just hard rocking nuts from Phoenix. They had originally been called The Beans when they arrived in San Francisco, but they changed their name and morphed into a parody of a deranged hard rock band, complete with costumes, props and dancers. In 1973, still playing the local clubs, they were much sloppier players, with low-rent props and stunts, but that of course added to the "performance art" aspect of portraying a deranged and debauched hard rock band with pretensions towards English glam rock. The band that would perform on their debut album (and next several) in 1975 was already intact, including future Grateful Dead keyboardist Vince Welnick.
The new Matrix did not last much beyond this show--and indeed how could you top a week of the Wailers, Graham Central Station (on the 26th and 27th, above) and then Iggy and The Stooges with The Tubes? The venue became a soul club called The Soul Train (after the TV show), and then hosted a play called Bullshot Crummond (which I believe I saw) and finally from 1980 to 1990 it was The Stone. The Stone was linked to the Keystone Berkeley and Keystone Palo Alto, and was an important part of the Bay Area rock scene in the 1980s.
Currently the venue is the home of a club called Broadway Showgirls Cabaret (don't google it at work).