For questions about matrices which are defined block wise, like $\pmatrix{A&B\ C&D}$ where $A,B,C$ and $D$ are themselves matrices. Use this tag with (matrices), and often with (linear-algebra).
Questions tagged [block-matrices]
908 questions
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Subset of $GL(n,R)$
I'm trying to understand why the subset of $GL(n,\mathbb{R})$ formed by the block-matrices of the following type:
$$\begin{pmatrix} A & B \\ 0 & C \end{pmatrix}$$ where
$$A \in GL(k,\mathbb{R}),~ C \in GL(n-k,\mathbb{R}),~ B \in…
Br09
- 2,140
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0 answers
when block matrix is positive definite ,
can one tell me when the block matrix M=[A B,C D] is positive definite such as:
1-the four block A,B,C and D are symmetric diagonal positive definite matrices
2-M is asymmetric, so C is not the transpose of B, and we can not apply schur formula
fidel
- 31
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Characteristic polynomial of triangular blocks matrix
Let A be a triangular blocks matrix (the blocks are: A1,...,Ak).
Show that CA(t)=CA1(t)*...*CAk(t).
Any help ? thanks ;)
(edit: CA and CAj are the characteristic polynomials of the blocks)
Jenni201
- 463
- 2
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- 12
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Product of the off-diagonal block matrices
Consider two real symmetric positive matrices $A\geq0$ and $B\geq 0$ with the following block form
\begin{equation}
A=
\begin{pmatrix}\begin{array}{@{}c|c@{}}
A_{11} & A_{12} \\ \hline
A_{21} & A_{22} \\
\end{array}\end{pmatrix}, \quad…
tamih100
- 1
0
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1 answer
Determinant and Inverse of a block matrix with diagonal blocks
So I want to calculate the inverse and determinant of a block matrix ($n\times n$) with diagonal matrices (of same size) as block.
Although I have a general idea as to how to calculate the determinant. I can't find anything relevant to find the…
Manu S Pillai
- 101