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- ...e matrix <math>T=
</math>. This matrix has non-negative entries and all its rows and columns add up to <math>1</ma The first goal of the proof is to show that there is a ''doubly stochastic matrix'' <math>D</math> such that <math>q=Dp</math>. Then [https://en.wikipedia.or8 KB (1,346 words) - 11:53, 8 October 2023 - Notice that this problem can be converted into a Markov Chain transition matrix. The transition matrix is { {0,1,1}, {1,0,1} , {1,1,0} } * (1/2) . Then use the exponentiation met15 KB (2,406 words) - 22:56, 23 November 2023
- ...>A</math> as a matrix, which is essentially the adjacency matrix where the diagonal is changed to be <math>1</math> whenever the degree is odd; in more technic ...th>A</math> consists of <math>1</math>s, so this says that the size of the diagonal of this submatrix is even. But this is also the number of <math>v</math> su13 KB (2,414 words) - 13:37, 11 July 2016
- ...lumn is <math>\geq n</math>. Prove that the sum of all the elements of the matrix is <math>\geq n^2 / 2</math>. ...w z \ge n - S</math>. The total sum <math> T</math> of all elements of the matrix is at least the number of zeros in this row multiplicated by <math> n - S</6 KB (1,192 words) - 13:14, 29 January 2021
- For an <math>n\times n</math> matrix <math>a = (a_{ij})</math>, the determinant is defined by For example, the determinant of a <math>2\times 2</math> matrix8 KB (1,345 words) - 23:31, 8 May 2020
- ...ath>. Here, <math>I</math> refers to the <math>n\times n</math> [[identity matrix]]. ...bda I-A) = 0</math>, then the column vectors of the <math>n\times n</math> matrix <math>\lambda I - A</math> are linearly dependent. Indeed, if we define <ma19 KB (3,412 words) - 13:57, 21 September 2022
- ...lements of the main diagonal of the matrix. For example, the trace of the matrix <math>M =
<759 bytes (120 words) - 18:27, 2 March 2010 - ...matrices]] <math>A,B</math> are '''similar''' if there exists an [[unitary matrix]] <math>U</math> such that <math>B = U^{-1}AU</math>. ...s, then it has a basis of eigenvectors and will be similar to a [[diagonal matrix]].342 bytes (60 words) - 18:53, 2 March 2010
- ...''' is a <math>n \times n</math> matrix with <math>1</math>s in its [[main diagonal]] and <math>0</math>s in every other entry. It is usually denoted <math>I_n ...trix inverse|inverse]] <math>A^{-1}</math> of <math>A</math> is the unique matrix such that <math>AA^{-1} = A^{-1}A = I_n</math>.1 KB (178 words) - 23:00, 16 March 2010
- Define a <i>T-grid</i> to be a <math>3\times3</math> matrix which satisfies the following two properties: Let three-in-a-row/column/diagonal be a "win" and let player <math>0</math> be the one that fills in <math>0</7 KB (1,330 words) - 21:42, 19 January 2025
- ...s in <math>M_n</math> are zero. Let <math>D_n</math> be the determinant of matrix <math>M_n</math>. Then <math>\sum_{n=1}^{\infty} \frac{1}{8D_n+1}</math> ca ...ath> is <math>a</math>, and the determinant of the <math>2 \times 2</math> matrix <math>\left[ {\begin{array}{cc}8 KB (1,301 words) - 07:43, 11 October 2020
- ...rem like solution 4, it is critical to know whether <math>OP</math> is the diagonal or side of quadrilateral. Equation for wrong case cannot be solved. For exa ==Solution 8 (Analytic- Can use complex numbers or rotation matrix)==13 KB (1,989 words) - 12:10, 8 December 2024
- ...of two of <math>M_1,M_2,</math> and <math>M_3</math> is equal to the third matrix.</li><p> ..., we cannot have one vector <math>(1,1,1)</math> and another one that is a diagonal vector on the plane that is perpendicular to the first selected vector.13 KB (2,072 words) - 00:22, 24 September 2024
- ...ant of the transpose of a matrix equals to the determinant of the original matrix. ...either be <math>\sqrt{21}</math> or <math>\sqrt{31}</math> because it is a diagonal. If <math>CD = \sqrt{21}</math>, applying the Law of Cosines on <math>\angl16 KB (2,614 words) - 18:35, 28 December 2024