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Swapping two rows, Multiplying a row by a nonzero number, Adding a multiple of one row to another row. Using these operations, a matrix can always be transformed into an upper triangular matrix (possibly bordered by rows or columns of zeros), and in fact one that is in row echelon form.
Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
Off-by-one errors are common in using the C library because it is not consistent with respect to whether one needs to subtract 1 byte – functions like fgets() and strncpy will never write past the length given them (fgets() subtracts 1 itself, and only retrieves (length − 1) bytes), whereas others, like strncat will write past the length given them.
Reducing the range of any index to a single value effectively eliminates that index. This feature can be used, for example, to extract one-dimensional slices (vectors: in 3D, rows, columns, and tubes [1]) or two-dimensional slices (rectangular matrices) from a three-dimensional array. However, since the range can be specified at run-time, type ...
Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.. The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
Here the number of initial conditions necessary for obtaining a closed form solution is the dimension n = 1 times the order k, or simply k. In this case the k initial pieces of information will typically not be different values of the variable x at different points in time, but rather the values of x and its first k – 1 derivatives, all at ...
About 68% of values drawn from a normal distribution are within one standard deviation σ from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. [8] This fact is known as the 68–95–99.7 (empirical) rule, or the 3-sigma rule.
Select all the rows from the beginning of the table to the last row to display ({begin_base_0 + rows}) Read the {begin_base_0 + rows} rows but send to display only when the row_number of the rows read is greater than {begin_base_0}