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The goal of the game is to fully fill in the given grid (3x3, 4x4, 5x5 ...) with missing numbers observing three simple rules. Rule #1 Each row must contain different numbers. Rule #2 Each column must contain different numbers. Rule #3 Each stream must contain different numbers.
In linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space.For example, using the convention below, the matrix = [ ]
The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3. In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.
For instance, the Lo Shu Square – the unique 3 × 3 magic square – is associative, because each pair of opposite points form a line of the square together with the center point, so the sum of the two opposite points equals the sum of a line minus the value of the center point regardless of which two opposite points are chosen. [4]
To denote a sequence of moves on the 3×3×3 Rubik's Cube, this article uses "Singmaster notation", [4] which was developed by David Singmaster. The following are standard moves, which do not move centre cubies of any face to another location:
Finding low-rank decompositions of such tensors (and beyond) is NP-hard; optimal multiplication even for 3x3 matrices remains unknown, even in commutative field. [24] On 4x4 matrices, AlphaTensor unexpectedly discovered a solution with 47 multiplication steps, an improvement over the 49 required with Strassen’s algorithm of 1969, albeit ...
Kron reduction is a useful tool to eliminate unused nodes in a Y-parameter matrix. [2] [3] For example, three linear elements linked in series with a port at each end may be easily modeled as a 4X4 nodal admittance matrix of Y-parameters, but only the two port nodes normally need to be considered for modeling and simulation.