Comments on: Matrix identities as derivatives of determinant identities
https://terrytao.wordpress.com/2013/01/13/matrix-identities-as-derivatives-of-determinant-identities/
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoMon, 21 May 2018 20:43:45 +0000hourly1http://wordpress.com/By: Anonymous
https://terrytao.wordpress.com/2013/01/13/matrix-identities-as-derivatives-of-determinant-identities/#comment-487698
Tue, 17 Oct 2017 18:51:50 +0000http://terrytao.wordpress.com/?p=6439#comment-487698Is there any book which discusses this stuff and particularly identity 4 and its corresponding identity
]]>By: Inverting the Schur complement, and large-dimensional Gelfand-Tsetlin patterns | What's new
https://terrytao.wordpress.com/2013/01/13/matrix-identities-as-derivatives-of-determinant-identities/#comment-486308
Sat, 16 Sep 2017 22:07:59 +0000http://terrytao.wordpress.com/?p=6439#comment-486308[…] the other hand, by the Woodbury matrix identity (discussed in this previous blog post), we […]
]]>By: Dodgson condensation from Schur complementation | What's new
https://terrytao.wordpress.com/2013/01/13/matrix-identities-as-derivatives-of-determinant-identities/#comment-485539
Mon, 28 Aug 2017 21:17:32 +0000http://terrytao.wordpress.com/?p=6439#comment-485539[…] can in turn be used to establish many further identities; in particular, as shown in A HREF=”https://terrytao.wordpress.com/2013/01/13/matrix-identities-as-derivatives-of-determinant-identities… previous post, it implies the Schur determinant […]
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https://terrytao.wordpress.com/2013/01/13/matrix-identities-as-derivatives-of-determinant-identities/#comment-484174
Mon, 24 Jul 2017 07:25:38 +0000http://terrytao.wordpress.com/?p=6439#comment-484174Is it possible to have any such derivations for permanent-trace or permanent-determinant?
]]>By: 起源笔记 / 基于云数据的网络松鼠症分布模型设计一文
https://terrytao.wordpress.com/2013/01/13/matrix-identities-as-derivatives-of-determinant-identities/#comment-481762
Sun, 04 Jun 2017 08:06:55 +0000http://terrytao.wordpress.com/?p=6439#comment-481762[…] a scalar such that is non-zero. (See also this previous blog post for more discussion of these sorts of […]
]]>By: Quantitative continuity estimates | What's new
https://terrytao.wordpress.com/2013/01/13/matrix-identities-as-derivatives-of-determinant-identities/#comment-481108
Tue, 23 May 2017 01:55:34 +0000http://terrytao.wordpress.com/?p=6439#comment-481108[…] is a scalar such that is non-zero. (See also this previous blog post for more discussion of these sorts of […]
]]>By: Pascal
https://terrytao.wordpress.com/2013/01/13/matrix-identities-as-derivatives-of-determinant-identities/#comment-479589
Tue, 04 Apr 2017 02:31:06 +0000http://terrytao.wordpress.com/?p=6439#comment-479589Hi, may i know is there any analytic formula for the derivative of adjugate matrix w.r.t itself or its elements? i.e.

or

]]>By: Derived multiplicative functions | What's new
https://terrytao.wordpress.com/2013/01/13/matrix-identities-as-derivatives-of-determinant-identities/#comment-419783
Wed, 24 Sep 2014 22:29:06 +0000http://terrytao.wordpress.com/?p=6439#comment-419783[…] identities, such as (1). This phenomenon is analogous to the one in linear algebra discussed in this previous blog post, in which many of the trace identities used there are derivatives of determinant identities. For […]
]]>By: My Math Diary
https://terrytao.wordpress.com/2013/01/13/matrix-identities-as-derivatives-of-determinant-identities/#comment-305632
Sun, 20 Apr 2014 17:50:27 +0000http://terrytao.wordpress.com/?p=6439#comment-305632[…] Derivative of determinant: Terry Tao, Stack […]
]]>By: Anonymous
https://terrytao.wordpress.com/2013/01/13/matrix-identities-as-derivatives-of-determinant-identities/#comment-269307
Sat, 01 Feb 2014 18:37:11 +0000http://terrytao.wordpress.com/?p=6439#comment-269307The identity det(X + Y) = det(X) + det(Y) – tr(XY) + tr(X)tr(Y) is a special case of the identity described in Reutenauer and Schuetzenberger’s paper giving the determinant of the sum of k square matrices of order n as a sum of k^n terms. For example, if X and Y are 3×3 matrices then det(X + Y) = det(X) + det(Y) – tr(XY)tr(X) – tr(XY)tr(Y) + c(X)tr(Y) + tr(X)c(Y) + tr(XXY) + tr(XYY) , where c(X) = (tr(X)^2 – tr(X^2)) / 2.
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