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– size of an SSE vector register, included as part of the x86-64 standard 160 bits (20 bytes) – maximum key length of the SHA-1, standard Tiger (hash function), and Tiger2 cryptographic message digest algorithms 2 8: 256 bits (32 bytes) – minimum key length for the recommended strong cryptographic message digests as of 2004
Thus one will expect to be within 1 ⁄ 8 to 8 times the correct value – within an order of magnitude, and much less than the worst case of erring by a factor of 2 9 = 512 (about 2.71 orders of magnitude). If one has a shorter chain or estimates more accurately, the overall estimate will be correspondingly better.
Scale analysis (or order-of-magnitude analysis) is a powerful tool used in the mathematical sciences for the simplification of equations with many terms. First the approximate magnitude of individual terms in the equations is determined.
When truncating, a number of this order of magnitude is between 10 6 and 10 7. In a similar example, with the phrase "seven-figure income", the order of magnitude is the number of figures minus one, so it is very easily determined without a calculator to be 6. An order of magnitude is an approximate position on a logarithmic scale.
In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
To help compare different orders of magnitude, this section lists lengths between 10 −9 and 10 −8 m (1 nm and 10 nm). 1 nm – diameter of a carbon nanotube 1 nm – roughly the length of a sucrose molecule, calculated by Albert Einstein
By definition, all Euclidean vectors have a magnitude (see above). However, a vector in an abstract vector space does not possess a magnitude. A vector space endowed with a norm, such as the Euclidean space, is called a normed vector space. [8] The norm of a vector v in a normed vector space can be considered to be the magnitude of v.
A bound vector is defined as the combination of an ordinary vector quantity and a point of application or point of action. [ 1 ] [ 4 ] Bound vector quantities are formulated as a directed line segment , with a definite initial point besides the magnitude and direction of the main vector.