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The Ansoff matrix is a strategic planning tool that provides a framework to help executives, senior managers, and marketers devise strategies for future business growth. [1] It is named after Russian American Igor Ansoff , an applied mathematician and business manager, who created the concept.
Market penetration is the key for a business growth strategy stemming from the Ansoff Matrix (Richardson, M., & Evans, C. (2007). H. Igor Ansoff first devised and published the Ansoff Matrix in the Harvard Business Review in 1957, within an article titled "Strategies for Diversification". The grid/matrix is utilized across businesses to help ...
In mathematics, every analytic function can be used for defining a matrix function that maps square matrices with complex entries to square matrices of the same size. This is used for defining the exponential of a matrix , which is involved in the closed-form solution of systems of linear differential equations .
The elementary functions are constructed by composing arithmetic operations, the exponential function (), the natural logarithm (), trigonometric functions (,), and their inverses. The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's ...
Ansoff pointed out that a diversification strategy stands apart from the other three strategies. Whereas, the first three strategies are usually pursued with the same technical, financial, and merchandising resources used for the original product line, the diversification usually requires a company to acquire new skills and knowledge in product development as well as new insights into market ...
Whitening a data matrix follows the same transformation as for random variables. An empirical whitening transform is obtained by estimating the covariance (e.g. by maximum likelihood) and subsequently constructing a corresponding estimated whitening matrix (e.g. by Cholesky decomposition).
When A is an invertible matrix there is a matrix A −1 that represents a transformation that "undoes" A since its composition with A is the identity matrix. In some practical applications, inversion can be computed using general inversion algorithms or by performing inverse operations (that have obvious geometric interpretation, like rotating ...
Harry Igor Ansoff (Russian: Игорь Ансов; 12 December 1918 – 14 July 2002) was a Russian American applied mathematician and business manager. [1] He is known as one of the fathers of strategic management .