The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



a rectangular array of (m X n) elements (numbers) arranged in m columns and n rows:

The Krakówian, introduced in the 1920’s by the Polish astronomer T. Banachiewicz (1882–1954), differs from ordinary matrices used in linear algebra by a simpler multiplication rule. We multiply the columns of cofactors having the same number of rows:

Here rb is the transposed krakowian of b. Furthermore, operations such as division and extraction of a square root, which are lacking in matrix algebra, can be performed on Krakowians. Krakowians have found application in geodetic calculations.


Modrinskii, N. I. Primenenie krakovianov v geodezicheskikh vychisleniiakh. Moscow, 1959.
Zlatanov, G. Krakovianovo smiatane. Sofia, 1968.
Banachiewicz, T. Rachunek krakowianowy z zastosowaniami. Warsaw, 1959.


The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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