Diagonal matrixIn linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is [3002]{\displaystyle \left[{\begin{smallmatrix}3&0\\0&2\end{smallmatrix}} ight]}, while an example of a 3×3 diagonal matrix is[600050004]{\displaystyle \left[{\begin{smallmatrix}6&0&0\\0&5&0\\0&0&4\end{smallmatrix}} ight]}.
Square matrixIn mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n{\displaystyle n}. Any two square matrices of the same order can be added and multiplied. Square matrices are often used to represent simple linear transformations, such as shearing or rotation.
LU decompositionType of matrix factorizationIn numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix multiplication and matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination.
Matrix multiplicationIn mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB.
Minor (linear algebra)In linear algebra, a minor of a matrixA is the determinant of some smaller square matrix generated from A by removing one or more of its rows and columns. Minors obtained by removing just one row and one column from square matrices (first minors) are useful for calculating matrix cofactors, which are useful for computing both the determinant and inverse of square matrices.
Bootstrapping (finance)In finance, bootstrapping is a method for constructing a (zero-coupon) fixed-income yield curve from the prices of a set of coupon-bearing products, e.g. bonds and swaps. A bootstrapped curve, correspondingly, is one where the prices of the instruments used as an input to the curve, will be an exact output, when these same instruments are valued using this curve.
Main diagonalIn linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a matrixA{\displaystyle A} is the list of entries ai,j{\displaystyle a_{i,j}} where i=j{\displaystyle i=j}. All off-diagonal elements are zero in a diagonal matrix.
Invertible matrixIn linear algebra, an invertible matrix (non-singular, non-degenerate or regular) is a square matrix that has an inverse. In other words, if a matrix is invertible, it can be multiplied by its inverse matrix to yield the identity matrix. Invertible matrices are the same size as their inverse.
TrapezoidIn geometry, a trapezoid () in North American English or trapezium () in British English is a quadrilateral that has at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid. The other two sides are called the legs or lateral sides. If the trapezoid is a parallelogram, then the choice of bases and legs is arbitrary. A trapezoid is usually considered to be a convex quadrilateral in Euclidean geometry, but there are also crossed cases.
Numerical analysisNumerical analysis is the study of algorithms for the problems of continuous mathematics. These algorithms involve real or complex variables (in contrast to discrete mathematics), and typically use numerical approximation in addition to symbolic manipulation. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts.
If and only ifIn logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") states that the truth values of two statements are equal. It is paraphrased by the biconditional, a logical connective between statements. The biconditional is true in two cases, where either both statements are true or both are false.Matrix similarityIn linear algebra, two n-by-n matrices A and B are called similar if there exists an invertible n-by-n matrix P such that B = P − 1 A P . {\displaystyle B=P^{-1}AP.} Two matrices are similar if and only if they represent the same linear map under two possibly different bases, with P being the change-of-basis matrix.*As an Amazon Associate I earn from qualifying purchases.