By extension, it can mean an underworld abode of lost souls, or hell.

By extension, the term " embark " literally means to board the kind of boat called a " barque ".

By extension, the term is also used to refer to any system administrator who displays ( or wishes he could get away with ) the qualities of the original.

By extension, it has come to include an extreme and unreasoning partisanship on behalf of any group to which one belongs, especially when the partisanship includes malice and hatred towards rival groups.

By extension, the word for carrying or drawing a beer came to mean the serving of the beer and, in some senses, the act of drinking, or a drink of beer itself, regardless of serving method.

By extension, the term equinox may denote an equinoctial point.

By extension, it may be used for a decision to ignore the person or subject in other media.

By extension, in popular legend the palace is associated with the myth of the Minotaur.

By extension, it also has a role in guarding members of the judiciary, who administer justice in the name of the Prince.

By extension, the term " Old Mandarin " is used by linguists to refer to the northern dialects recorded in materials from the Yuan dynasty.

By extension, the term " manichean " is widely applied ( often disparagingly ) as an adjective to a philosophy or attitude of moral dualism, according to which a moral course of action involves a clear ( or simplistic ) choice between good and evil, or as a noun to people who hold such a view.

By extension, the term " mushroom " can also designate the entire fungus when in culture ; the thallus ( called a mycelium ) of species forming the fruiting bodies called mushrooms ; or the species itself.

By extension, other religions ' feasts are occasionally described by the same term.

By metaphoric extension, the term " movable feast " was used by Ernest Hemingway to mean the memory of a splendid place that continues to go with the moving traveler for the rest of life, after he has had the experience of it and gone away.

By extension, the word manor is sometimes used in England to mean any home area or territory in which authority is held, often in a police or criminal context.

By extension the term parish refers not only to the territorial unit but to the people of its community or congregation as well as to church property within it.

* By extension, a situation that is difficult to get out of.

By extension, the reader should not believe that the pair dies ; the reader is expected to accept that they are literary figures that live on today.

By extension the term self-determination has come to mean the free choice of one's own acts without external compulsion.

By extension, the term " snake oil salesman " may be applied to someone who sells fraudulent goods, or who is a fraud himself.

By extension from the Roman historical experience, some modern politicians have been called " Tribunes of the People.

By extension, " onshore trust " has come to mean any trust resident in a high-tax jurisdiction.

By 1920, a systematic program of extension work throughout northeast Iowa had begun, with Upper Iowa referred to as " a pioneer in the field.

By 1972, the clean and press was discontinued because athletes started to push with legs and bend backwards instead of strictly pressing the weight overhead, and this left the sole elements of what is today's modern Olympic weightlifting programme – the snatch and the clean and jerk. The snatch entails pulling with a wide grip the barbell overhead without pressing out with the arms. It is a very precise lift that can be nullified by a lack of balance of the athlete. The clean and jerk is more forgiving using a narrower grip pull the bar to the shoulders and then using the strength of the legs push until arms reach full extension without a press out.

By extension, moving an entire session from one X server to another is generally not possible.

By placing the molecules in wells in the gel and applying an electric field, the molecules will move through the matrix at different rates, determined largely by their mass when the charge to mass ratio ( Z ) of all species is uniform, toward the ( negatively charged ) cathode if positively charged or toward the ( positively charged ) anode if negatively charged.

: By looking at the final matrix ( reduced row-echelon form ) one could see that the first non-zero entry in both and is a.

By switching the looping order for and, the speedup in large matrix multiplications becomes dramatic.

By Euler's rotation theorem, we may replace the vector with where is a 3x3 rotation matrix and is the position of the particle at some fixed point in time, say t = 0.

By definition, the matrix with general element

By the definition of unitary matrix, the same is true for their conjugate transposes U * and V. In short, U, U *, V, and V * are orthonormal bases.

By separable, we mean that a matrix can be written as an outer product of two vectors, or, in coordinates,.

By our assumption, the matrix associated to a list of intervals will remain essentially unchanged from one time step to the next.

By implicit function theorem, the variety is a manifold in the neighborhood of a point of it where the Jacobian matrix has rank k. At such a point P, the normal vector space is the vector space generated by the values at P of the gradient vectors of the f < sub > i </ sub >.

By simplifying the quaternion multiplications, they can be rewritten as a rotation matrix given an axis-angle representation:

By the finite-dimensional spectral theorem, such operators can be associated with an orthonormal basis of the underlying space in which the operator is represented as a diagonal matrix with entries in the real numbers.

By choosing another basis, the Newton basis, we get a system of linear equations with a much simpler lower triangular matrix which can be solved faster.

By choosing another basis, the Lagrange basis, we get the much simpler identity matrix = δ < sub > i, j </ sub > which we can solve instantly: the Lagrange basis inverts the Vandermonde matrix.

By linearity of matrix multiplication, we have that

By 1969 Altshuller had reviewed about 40, 000 patent abstracts in order to find out in what way the innovation had taken place and developed the concept of technical contradictions, the concept of ideality of a system, contradiction matrix, and 40 principles of invention.

By way of contrast, sequence profiles are a type of scoring matrix that represents a similar set of patterns that includes insertions and deletions.

By comparison, KPCA begins by computing the covariance matrix of the data after being transformed into a higher-dimensional space,

By finding which combinations of frequency and wavenumber drive the determinant of the matrix to zero, the propagation characteristics of the medium may be determined.

By means of a finite sequence of elementary row operations, any matrix can be transformed to row echelon form.

By using the scoring matrix ( substitution matrix ) to score the comparison of each residue pair, there are 20 ^ 3 possible match scores for a 3-letter word.

By the LU decomposition algorithm, any invertible matrix may be written as the product of a lower triangular matrix L by an upper triangular matrix U.