text:
@sbonline
063-180-0826 ถึง 9
แทงบอล ฝาก-ถอน วิธีเล่น โปรโมชั่น สมัคร SBOBET ติดต่อเรา ทางเข้า SBOBET
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แจ้งฝาก-ถอน
ฝาก ถอน
ฟุตบอลออนไลน์ อันดับ 1 ในประเทศไทย
www.sbobetsb.com คือเว็บไซต์ผู้ให้บริการต่างๆ จากทาง SBOBET THAILAND โดยทีมงานจากทาง sbobet โดยตรง หมดปัญหาเรื่องการโกง และยังสามารถ ตรวจสอบ user กับทาง บริษัท sbobet ได้ทั่วโลก และระบบ ฝาก-ถอน ที่มีมาตรฐาน ช่วยให้คุณเล่นด้วยความมั่นใจและปลอดภัย
5 out of 5.0 based on 255720 user ratings. คลิกเพื่อโหวต
แสดงความคิดเห็นเกี่ยวกับ Sbobetsb
ความคิดเห็นจากสมาชิก Sbobetsb
5 out of 5.0 based on 255720 user ratings.
ความพอใจ :
ความคิดเห็น : เวปนี้สุดยอดมากมายเลยครับผมมมมมมมมมมมมมมมมมมมมนะคับ88888888
โดย zutsbo4XXXX
ความคิดเห็น : ดีมากๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆๆ
ความคิดเห็น : มาก ดีมาก ดีมาก ดีมาก ดีมากๆๆๆ
ความคิดเห็น : สุดยอดโปรโมชั่นดีดีแบบนี้ชอบเล่นง่าย สนุก มีทั้งกีฬา บาคาร่า เกม เยอะมากต้องลองไม่ผิดหวังเลยค่ะที่มาเล่นกับที่นี่ บริการดีมากค่ะ
ความคิดเห็น : สำหรับวงการเว็ปบอลไม่มีใครกล้าแจกจริงๆแบบนี้ อยู่นานๆนะเที่ยงตรง โอนจริง จ่ายจริง ปลอดภัย ระบบการจัดการดีสำหรับวงการเว็ปบอลไม่มีใครกล้าแจกจริงๆแบบนี้ อยู่นานๆนะเที่ยงตรง โอนจริง จ่ายจริง ปลอดภัย ระบบการจัดการดีเยี่ยม พงลาดได้ไงต้องลองเป็นเว็ปไซต์ที่ให้ผลตอบแทนที่ดี พงลาดได้ไงต้องลองเป็นเว็ปไซต์ที่ให้ผลตอบแทนที่ดี5ที่สุด5555555555555555555555555555555555555555555666666666666
ความคิดเห็น : เนื้อเพลง ผู้บ่าวเก่า - เต๊ะ ตระกูลตอ คิดว่าดีที่ตัดสินใจเลิกกับเจ้าในมื้อนั้น ย้อนเหตุผลคือสองเฮามันบ่เข้าใจกัน แรก ๆ อ้ายกะอยู่ได้ บ่ได้คิดอีหยัง ผ่านไปนาน ๆ หัวใจอ้ายนั้นเริ่มห่วงหา ว่าสิขอคืนดีแต่เสียทีน้องรับคนใหม่เข้ามา นอนเสียดายเวลา น้ำตาอ้ายมันก็ไหลซึม ๆ น้องกะคงสิลืม แต่ว่าอ้ายบ่ลืม มันฮักตื่มพุ่นใจของอ้าย ตอนคบกันกะยอมรับว่ามันเบื่อ พอเลิกกันไปละเหลือใจเจ้าของ ว่าเป็นหยังคือปล่อยให้น้อง ไปเป็นของเขา อยากบอกฮักอ้ายกะเฮ็ดบ่ได้ ยามคิดฮอดอยากกอดกะได้แค่คิด อยากเว้านำสักคำแต่อ้ายกะบ่มีสิทธิ์ มันติดที่ว่าเฮาเป็นผู้บ่าวเก่า อยากหอมแก้มกะได้แค่แนมด้วยสายตา น้ำมันไหลออกตาย้อนว่าฐานะเราบ่คือเก่า อ้ายนั่งไห้เป็นทุกข์น้องเป็นสุขฮักกันกับเขา กะฮักผู้บ่าวใหม่ ย้อนคำว่าบ่ฮักมันคืออุปสรรคของอ้าย น้องกะมีผู้บ่าวใหม่ อ้ายกะเป็นผู้บ่าวเก่า น้องบ่ได้ไปไสยังอยู่ในใจอ้ายคือเก่า ถึงแม้เฮาสิเลิกกันไปกะบ่ได้แปลว่าเซาฮัก ซุมื้อนี้อ้ายยังบ่ทันมีไผในใจนอกจากเจ้า ซุมื้อนี้เจ้ามีเขาน้องนอนเหงาอยู่บักคัก เรื่องของเราสองเฮากะคงสิเป็นกันได้ยาก เพราะน้องเซาฮักกันแล้ว ตอนคบกันกะยอมรับว่ามันเบื่อ พอเลิกกันไปละเหลือใจเจ้าของ ว่าเป็นหยังคือปล่อยให้น้อง ไปเป็นของเขา อยากบอกฮักอ้ายกะเฮ็ดบ่ได้ ยามคิดฮอดอยากกอดกะได้แค่คิด อยากเว้านำสักคำแต่อ้ายกะบ่มีสิทธิ์ มันติดที่ว่าเฮาเป็นผู้บ่าวเก่า อยากหอมแก้มกะได้แค่แนมด้วยสายตา น้ำมันไหลออกตาย้อนว่าฐานะเราบ่คือเก่า อ้ายนั่งไห้เป็นทุกข์น้องเป็นสุขฮักกันกับเขา กะฮักผู้บ่าวใหม่ อยากบอกฮักอ้ายกะเฮ็ดบ่ได้ ยามคิดฮอดอยากกอดกะได้แค่คิด อยากเว้านำสักคำแต่อ้ายกะบ่มีสิทธิ์ อยากหอมแก้มกะได้แค่แนมด้วยสายตา น้ำมันไหลออกตาย้อนว่าฐานะเราบ่คือเก่า อ้ายนั่งไห้เป็นทุกข์น้องเป็นสุขฮักกันกับเขา กะฮักผู้บ่าวใหม่ ตั้งแต่เราเลิกกันมันทรมานแทบอยู่บ่ได้ จากใจผู้บ่าวเก่า
ความคิดเห็น : ♥เว็บไซต์ดีมีคุณภาพให้บริการทางด้านกีฬามีหลากหลายให้เลือกเล่นตลอดทุกวันทุก 24 ชั่วโมงสุดสุดแล้ว
ความคิดเห็น : ชอบกิจกรรมนี้มากความ เว็บก็เจ๋งมากกกกกกกกกกกกเลย
ความคิดเห็น : ยอร์เกน คล็อปป์ ผู้จัดการทีม ลิเวอร์พูล ได้ปฏิเสธที่จะให้ สตีเวน เจอร์ราร์ด ยืมตัว ไรอัน เคนท์ ไปใช้ที่ กลาสโกว เรนเจอร์ส ตามรายงานของ เดอะ มิร์เรอร์ เจอร์ราร์ด สนใจที่จะดึง เคนท์ มายังถิ่น ไอบอร์กซ์ อีกครั้ง หลังฤดูกาลก่อน ลิเวอร์พูล ได้ให้พวกเขายืมตัวมาและสามารถทำผลงานได้อย่างน่าประทับใจ
ความคิดเห็น : ดีมากๆเลยอ่ะ สำหรับวงการเว็ปบอลไม่มีใครกล้าแจกจริงๆแบบนี้ อยู่นานๆนะ คนจะได้มาเล่นเยอะๆ ถ้าโปรแบบนี้อยู่นานๆ
ความคิดเห็น : บริการดีจริงๆครับ ปลอดภัยไร้กังวล ได้เงินชัวร์ สมัครมาเล่นด้วยกันเยอะๆนะ
ความคิดเห็น : เว็บไซต์อันดับหนึ่งแห่งวงการกีฬามีกีฬาตลอดทุกวันมากมายหลายลีก
ความคิดเห็น : เข้ามาสมัครเล่นกันนะครับมีโปรโมชั่นสำหรับสมาชิกใหม่เพียบๆๆเลยครับรับรองเล่นใจแน่นอนครับ
ความคิดเห็น : ปรับโปรใหม่ทำยอดเล่นเพิ่มเยอะเกินไป
ความคิดเห็น : บริการดีมากชอบมากเลยเว็บบอลที่มีเกมส์มีโบนัดแจกมากมาย
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Q: Proof all eigenvalues of $P+(I-P)C$ are with positive real parts. $P=\frac{1}{n}\mathbf{1}\mathbf{1}^T$($\mathbf{1}=[1,1,\dots,1]^T$), $I\in R^n$ is a indentity matrix, $C\in R^{n\times n}$ is a symmetric positive definite matrix. Are all eigenvalues of $P+(I-P)C$ with positive real parts? How to prove that? (In other words, we should prove $rank(P+(I-P)C)=n$ and its all eigenvalues are with positive real parts)
With a random positive definite symmetric matrix $C$, I did 10 million experiments. All eigenvalues of $P+(I-P)C$ are with positive real parts.
Besides, I already prove that $P+(I-P)C$ is unsymmetrical.

A: Here is a brief answer that you will need to fill some details in.

*

*Pick a new ON-basis such that $\frac{1}{\sqrt{n}}\mathbf{1}$ is the first basis vector $[1,0,\ldots,0]^T$. No need to perform the change explicitly, all you need is to know how $P$ and $I-P$ looks like in the new basis.

*The positive definite $C$ becomes a new positive definite matrix $C'$ that we partition  as
$$
C'=\left[\begin{array}{c|c}q & r^T\\\hline r & S\end{array}\right],\quad q\in\Bbb{R},\ S\in\Bbb{R}^{(n-1)\times(n-1)}.
$$
Prove that $S$ is positive definite.

*The matrix in question in the new basis becomes
$$
\left[\begin{array}{c|c}1 & 0^T\\\hline r & S\end{array}\right].
$$
Prove that all its eigenvalues are positive.

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