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Page "Determinant" ¶ 21
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If and matrix
If there are proteins left in the shell matrix, it is also possible that they can trigger an allergic ( asthmatic ) attack.
If A is expressed as an N × N matrix, then A < sup >†</ sup > is its conjugate transpose.
If matrix support is polar ( e. g. paper, silica etc.
If the condition number is close to one, the matrix is well conditioned which means its inverse can be computed with good accuracy.
If the condition number is large, then the matrix is said to be ill-conditioned.
If we write an n-by-n matrix in terms of its column vectors
If G = GL < sub >*</ sub >( K ), then the set of natural numbers is a proper subset of G < sub > 0 </ sub >, since for each natural number n, there is a corresponding identity matrix of dimension n. G ( m, n ) is empty unless m = n, in which case it is the set of all nxn invertible matrices.
If is a quaternion valued spinor, is quaternion hermitian 4x4 matrix coming from Sp ( 8 ) and is a pure imaginary quaternion ( both of which are 4-vector bosons ) then the interaction term is:
If the 3 generations are then put in a 3x3 hermitian matrix with certain additions for the diagonal elements then these matrices form an exceptional ( grassman -) Jordan algebra, which has the symmetry group of one of the exceptional Lie groups ( F < sub > 4 </ sub >, E < sub > 6 </ sub >, E < sub > 7 </ sub > or E < sub > 8 </ sub >) depending on the details.
If he used the punch and matrix approach, all his letters should have been nearly identical, with some variations due to miscasting and inking.
If G is any subgroup of GL < sub > n </ sub >( R ), then the exponential map takes the Lie algebra of G into G, so we have an exponential map for all matrix groups.
* If the message indicates, Bob would send his qubit through the unitary gate given by the Pauli matrix
If one considers the matrix A as a linear mapping
* If A is a square matrix ( i. e., m = n ), then A is invertible if and only if A has rank n ( that is, A has full rank ).
* If B is any n-by-k matrix, then
* If B is an n-by-k matrix with rank n, then
* If C is an l-by-m matrix with rank m, then
* Sylvester ’ s rank inequality: If A is a m-by-n matrix and B n-by-k, then
If the impression is made purely as a relief resulting from the greater pressure on the paper where the high parts of the matrix touch, the seal is known as a dry seal ; in all other cases a liquid or liquified medium ( such as ink or wax ) is used, usually in another color than the paper.
If A is a matrix,
If the matrix is positive semidefinite matrix, then is a convex function: In this case the quadratic program has a global minimizer if there exists some feasible vector ( satisfying the constraints ) and if is bounded below on the feasible region.
If the matrix is positive definite and the problem has a feasible solution, then the global minimizer is unique.

If and entries
* Haki Stërmilli's novel If I Were a Boy ( 1936 ) is written in the form of diary entries which documents the life of the main protagonist.
If each character is stored in 8 bits ( as in ASCII or ISO Latin 1 ), the table has only 2 < sup > 8 </ sup > = 256 entries ; in the case of Unicode characters, the table would have 17 × 2 < sup > 16 </ sup > = 1114112 entries.
< li > If M = ( m < sub > ij </ sub >) ≥ 0 then the diagonal entries m < sub > ii </ sub > are real and non-negative.
The first stage of boot loaders located on fixed disks and removable drives must fit into the first 446 bytes of the Master Boot Record in order to leave room for the default 64-byte partition table with four partition entries and the two-byte boot signature, which the BIOS requires for a proper boot loader — or even less, when additional features like more than four partition entries ( up to 16 with 16 bytes each ), a disk signature ( 6 bytes ), a disk timestamp ( 6 bytes ), an Advanced Active Partition ( 18 bytes ) or special multi-boot loaders If an active partition is found, the MBR code loads the boot sector code from that partition, known as Volume Boot Record ( VBR ), and executes it.
If, instead of 1 matching entry, there are k matching entries, the same algorithm works but the number of iterations must be π ( N / k )< sup > 1 / 2 </ sup >/ 4 instead of πN < sup > 1 / 2 </ sup >/ 4.
If we denote the-fold product of with itself by, then morphisms from to are m-by-n matrices with entries from the ring.
If there is more than one MX record with the same preference number, all of those must be tried before moving on to lower-priority entries.
If these dates are accurate, then it is unlikely that the earlier entries in the chronicle, starting with his arrival in Britain with his father Cerdic in 495, are correct.
If the position permits ( combined hands have sufficient number of intermediate cards, which can take the remaining tricks even if the three honors are played on the same trick ), it is often desirable to start by leading one of the high cards, in order to retain the lead in the same hand if the finesse is on, and spare the valuable entries.
If for some reason, e. g. a lack of entries, the menace cannot be unblocked, the squeeze becomes positional.
If the entries of the matrix are real or complex numbers ( or from any other commutative ring ), then all four quantities are equal.
If A and B have complex entries, then
If A has real entries and is symmetric ( or more generally, has complex-valued entries and is Hermitian ) and positive definite, then A can be decomposed as
If the table or file contained fixed length entries, the code could easily be converted to an absolute memory address or disk address for fast retrieval.
< li > If A has only real entries, then A < sup > T </ sup > A is a positive-semidefinite matrix.
If instead M is a 2n × 2n matrix with complex entries, the definition is not standard throughout the literature.
The Stylistics ' smooth sound also found an easier path onto adult contemporary airwaves than other soul artists, and the group made Billboard magazine's Easy Listening singles chart twelve times from 1971 to 1976, with three entries (" Betcha by Golly, Wow ", " You Make Me Feel Brand New ", and " You'll Never Get to Heaven ( If You Break My Heart )") reaching the Top 10.
The n < sup > 2 </ sup > functions g < sub > ij </ sub > form the entries of an n × n symmetric matrix, G. If
If a country only has one skater / team, that skater / team must place in the top ten to earn a second entry and in the top two to earn three entries to next year's championships.
If a country has two skaters / teams, the combined placement of those teams must be 13 or fewer to qualify 3 entries, and 28 or fewer to keep their two entries.

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