Linear algebra quick silly question

iScience
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so i just wanted to get this confirmed: the only two defined algebraic operations for matrices are addition and multiplication right?
 
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iScience said:
so i just wanted to get this confirmed: the only two defined algebraic operations for matrices are addition and multiplication right?
Perhaps you mean "arithmetic" rather than "algebraic" ?

How about subtraction?
 
i was including subtraction when i mentioned addition. and yes, "arithmetic" operations.

so that's all right? addition/subtraction and multiplication?
 
iScience said:
i was including subtraction when i mentioned addition. and yes, "arithmetic" operations.

so that's all right? addition/subtraction and multiplication?

In particular, division is not defined for matrices .
 
do transposes, traces, etc all count as algebraic operations?
 
iScience said:
do transposes, traces, etc all count as algebraic operations?
I don't know about the "algebraic" part, but they are certainly operations that are defined on matrices.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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