AT NOON TODAY, Sharon Pratt Dixon, whose vow to "clean house" captured the imagination of the electorate, takes office as mayor. It is an exhilarating moment for a capital city looking to shake off a singularly hurtful period in the 16 years of locally elected government. At the same time it is an anxious hour for a financially distressed city struggling to preserve its limited local franchise and to dispel myths about its ability to handle the powers accorded every other city in America.

Surely the city is right to expect progress under a new mayor who can put intelligence, talent and energy ahead of tired habits and old loyalties. Mrs. Dixon will look to a new D.C. Council, too, for help in winning over the federal government to a mission of solvency with efficiency. John A. Wilson, taking over as council chairman, understands the importance of a good executive-legislative partnership. There is value to a strong council presence, although the precarious state of home rule makes it necessary for Mr. Wilson to combine independent thinking with readiness for compromise at the District Building.

Another partnership must also be strengthened if the District is to be a strong contributor to a growing metropolitan region. As Mrs. Dixon has noted, the rescue of this city's troubled school system is essential and will demand a new chemistry between the mayor/council and the city's school board. Here, as in the case of the council, the voters have improved the membership. Here, too, the board's independence must be matched to the leadership role expected of the mayor in this central area of city policy.

The key to a successful District government is the ability of Mrs. Dixon to carry out her pledge to overhaul the bureaucracy and improve its efficiency and responsiveness. This is what the voters sought and what the federal government will demand before any further substantive help is forthcoming. It was this message of renaissance that Mrs. Dixon carried across the wards, color lines and economic differences in the city. This is the right way to assure Congress and the administration that their investment won't be squandered.

The Rivlin Commission has offered the new mayor a valuable guidebook for this mission, as well as indisputable evidence that the federal government has shortchanged the city. Commission members acknowledge that their recommendations are not the last word, but they have given the new mayor a head start on the job.

The spirit of this inaugural reflects the cross-section of Washingtonians who built the Sharon Dixon campaign. Citizens share her belief that an improved image of this city, around the world as well as close to home, can rekindle pride, fend off bankruptcy and strengthen the District's quest for a greater role in local and national decision-making. The stage is set for Mrs. Dixon to become a formidable force in renewing a grand capital city and hometown.