[Latex] Matrix and Determinant

本文详细介绍了三阶矩阵的表示方法及其对应的行列式计算过程。通过具体的数学公式展示了一个3x3矩阵及其行列式的写法。

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1. Matrix

\begin{equation}
  \left(
    \begin{array}{ccc}
    a&b&c\\
    d&e&f\\
    g&h&i
    \end{array}
  \right)
\end{equation}

result
这里写图片描述

2. Determinant

\begin{equation}
  \left|
    \begin{array}{ccc}
    a&b&c\\
    d&e&f\\
    g&h&i
    \end{array}
  \right|
\end{equation}

这里写图片描述

def qr(a, mode='reduced'): """ Compute the qr factorization of a matrix. Factor the matrix `a` as *qr*, where `q` is orthonormal and `r` is upper-triangular. Parameters ---------- a : array_like, shape (..., M, N) An array-like object with the dimensionality of at least 2. mode : {'reduced', 'complete', 'r', 'raw'}, optional If K = min(M, N), then * 'reduced' : returns Q, R with dimensions (..., M, K), (..., K, N) (default) * 'complete' : returns Q, R with dimensions (..., M, M), (..., M, N) * 'r' : returns R only with dimensions (..., K, N) * 'raw' : returns h, tau with dimensions (..., N, M), (..., K,) The options 'reduced', 'complete, and 'raw' are new in numpy 1.8, see the notes for more information. The default is 'reduced', and to maintain backward compatibility with earlier versions of numpy both it and the old default 'full' can be omitted. Note that array h returned in 'raw' mode is transposed for calling Fortran. The 'economic' mode is deprecated. The modes 'full' and 'economic' may be passed using only the first letter for backwards compatibility, but all others must be spelled out. See the Notes for more explanation. Returns ------- When mode is 'reduced' or 'complete', the result will be a namedtuple with the attributes `Q` and `R`. Q : ndarray of float or complex, optional A matrix with orthonormal columns. When mode = 'complete' the result is an orthogonal/unitary matrix depending on whether or not a is real/complex. The determinant may be either +/- 1 in that case. In case the number of dimensions in the input array is greater than 2 then a stack of the matrices with above properties is returned. R : ndarray of float or complex, optional The upper-triangular matrix or a stack of upper-triangular
03-26
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