Monthly Archives: April 2020

What Is Rounding?

Rounding is the transformation of a number expressed in a particular base to a number with fewer digits. For example, in base 10 we might round the number to , which can be described as rounding to three significant digits … Continue reading

Posted in what-is | 1 Comment

What Is a Random Orthogonal Matrix?

Various explicit parametrized formulas are available for constructing orthogonal matrices. To construct a random orthogonal matrix we can take such a formula and assign random values to the parameters. For example, a Householder matrix is orthogonal and symmetric and we … Continue reading

Posted in what-is | Leave a comment

What Is a Correlation Matrix?

In linear algebra terms, a correlation matrix is a symmetric positive semidefinite matrix with unit diagonal. In other words, it is a symmetric matrix with ones on the diagonal whose eigenvalues are all nonnegative. The term comes from statistics. If … Continue reading

Posted in what-is | Tagged | Leave a comment

What Is a Hadamard Matrix?

A Hadamard matrix is an matrix with elements and mutually orthogonal columns. For example, is a Hadamard matrix. A necessary condition for an Hadamard matrix to exist with is that is divisible by , but it is not known if … Continue reading

Posted in what-is | Leave a comment

What Is an Orthogonal Matrix?

A real, square matrix is orthogonal if (the identity matrix). Equivalently, . The columns of an orthogonal matrix are orthonormal, that is, they have 2-norm (Euclidean length) and are mutually orthogonal. The same is true of the rows. Important examples … Continue reading

Posted in what-is | Leave a comment

What Is a Generalized Inverse?

The matrix inverse is defined only for square nonsingular matrices. A generalized inverse is an extension of the concept of inverse that applies to square singular matrices and rectangular matrices. There are many definitions of generalized inverses, all of which … Continue reading

Posted in what-is | 3 Comments