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The exponential of a matrix A is defined by =!. Given a matrix B, another matrix A is said to be a matrix logarithm of B if e A = B.. Because the exponential function is not bijective for complex numbers (e.g. = =), numbers can have multiple complex logarithms, and as a consequence of this, some matrices may have more than one logarithm, as explained below.
In mathematics, the logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm.The logarithmic norm was independently introduced by Germund Dahlquist [1] and Sergei Lozinskiĭ in 1958, for square matrices.
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...
Krugersdorp (Afrikaans for Kruger's Town) is a mining city in the West Rand, Gauteng Province, South Africa founded in 1887 [2] by Marthinus Pretorius and Abner Cohen. [3] Following the discovery of gold on the Witwatersrand , a need arose for a major town in the west of the reef.
The town was established in 1890 to serve the new mine and was administered by Krugersdorp until it became a municipality in 1929. [ 2 ] : 292 Apart from having the largest stamp mill in the world, Randfontein, like many of the other outlying areas of Johannesburg, is essentially a rural collection of farms and small holdings in a particularly ...
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Sterkfontein, Cradle of Humankind Location in Gauteng Location Gauteng, South Africa Coordinates 26°00′57″S 27°44′05″E / 26.0157°S 27.7346°E / -26.0157; 27.7346 Established Declared a World Heritage Site in 2000 Governing body Cradle of Humankind Archaeologists in a structure above the entrance to Sterkfontein Sterkfontein (Afrikaans for Strong Spring) is a set of ...
Munsieville is a township situated in the Krugersdorp area in Gauteng Province, South Africa. It grew out of the informal settlements inhabited by mine laborers on the outskirts of the original mining town of Krugersdorp. The township was established by ordinance 58 of 1903 of the Krugersdorp municipality and called "the native location".