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  2. Rank–nullity theorem - Wikipedia

    en.wikipedia.org/wiki/Rank–nullity_theorem

    The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity of M ; and the dimension of the domain of a linear transformation f is the sum of the rank of f (the dimension of the image of f ) and the nullity of f (the dimension of the kernel of f ).

  3. Logical matrix - Wikipedia

    en.wikipedia.org/wiki/Logical_matrix

    A permutation matrix is a (0, 1)-matrix, all of whose columns and rows each have exactly one nonzero element.. A Costas array is a special case of a permutation matrix.; An incidence matrix in combinatorics and finite geometry has ones to indicate incidence between points (or vertices) and lines of a geometry, blocks of a block design, or edges of a graph.

  4. Row and column spaces - Wikipedia

    en.wikipedia.org/wiki/Row_and_column_spaces

    Thus Ax = 0 if and only if x is orthogonal (perpendicular) to each of the row vectors of A. It follows that the null space of A is the orthogonal complement to the row space. For example, if the row space is a plane through the origin in three dimensions, then the null space will be the perpendicular line through the origin.

  5. Rank (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Rank_(linear_algebra)

    It follows that Ax 1, Ax 2, …, Ax r are linearly independent. Now, each A x i is obviously a vector in the column space of A . So, A x 1 , A x 2 , …, A x r is a set of r linearly independent vectors in the column space of A and, hence, the dimension of the column space of A (i.e., the column rank of A ) must be at least as big as r .

  6. Propositional formula - Wikipedia

    en.wikipedia.org/wiki/Propositional_formula

    For example, suppose that an expression x begins with (. Starting after the second symbol, match the shortest subexpression y of x that has balanced parentheses. If x is a formula, there is exactly one symbol left after this expression, this symbol is a closing parenthesis, and y itself is a formula.

  7. Why is Tulane called the Green Wave? Nickname history ... - AOL

    www.aol.com/why-tulane-called-green-wave...

    What is a Green Wave? Here's what to know about the history of Tulane football's nickname ahead of American Conference championship game vs Army:

  8. Sisters Gave Birth 1 Day Apart at Same Hospital. Now They’re ...

    www.aol.com/sisters-gave-birth-1-day-233000574.html

    Mackenzie Root, 24, welcomed her daughter on Oct. 7 at Lakenau Medical Center — the next day, Alysha Orsine, 30, who works as a nurse at the same hospital, gave birth to her bundle of joy

  9. Matrix (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Matrix_(mathematics)

    An m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts.For example, a 2,1 represents the element at the second row and first column of the matrix.