feat(math): add first chapter linear algebruh

Areas/upv/classes/empresario/06-leading.md

@@ -0,0 +1,140 @@
+# 01 Managing or Leading?
+
+It is said that on one occasion Jack Welch, CEO of General Electric, summoned his immediate subordinates, gave them a maximum of three words:
+
+> "Don't lead, lead!"
+
+and then left the room. Many of them were plunged into absolute confusion:
+
+> "What is the difference?"
+
+
+# 02 Direction
+
+- Is seen as HR Management
+- It aims to achieve a joint action of the people who make up the organisation towards the achievement of common objectives.
+- It is essential because people are the key element in the company.
+- Try to make people's objectives compatible with those of the company, helping them meet their needs.
+
+Direction needs:
+- Leadership
+- Motivation
+- Communication
+
+# 03 Leadership
+
+>A leader has a vision and conviction that a dream can be achieved. He inspires the power and energy to get the job done.
+>–  Ralph Lauren
+
+**> Characteristics of a good leader**
+- Empathetic
+- Convincing
+- Creativ
+- Motivational
+- Selfcontrol
+- Delegates
+- Respectable
+- Sets an example
+- Obama
+
+**> Decalogue of the Good Boss**
+- Assumes his/hers responsibilities
+- Sets and example
+- Recognizes his or her own mistakes
+- Knows how to motivate and stimulate
+- Knows how to resolve conflcts
+- Promote the professional development of their employees
+- Treats their team with respect and consideration
+- Keeps a good working atmosphere
+- They know how to listen and are receptive to suggestions from others.
+- Knows how to delegate and trust
+- Is fair and balanced
+- is interested in the feelings of the people that work with them
+- Assures a good work/life balance for their employees
+- Doesn't act arrogant
+
+**> Has selfcontrol and emotional Intelligence**
+
+# What is emotional intelligence?
+It is a set of competencies (series of knowledge, skills and abilities and attitudes to do things effectively) related to the ability to adequately manage one's own emotions and also those of others.
+
+**> Emotional Awareness**
+The ability to be aware of you own and othere emotions
+
+**> Emotional Regulation**
+The ability to manage one's own emotions and those of others appropriately.
+
+**> Emotional Autonomy**
+broad competence that includes self-esteem, self-confidence, self-motivation, a positive attitude towards life, responsibility, the ability to critically analyze social norms, the ability to seek help and resources, critically evaluate the messages received, the ability to face adverse situations, etc.
+
+**> Socio-Emotional Skills**A
+ ability to maintain good relationships with others. (Assertiveness, empathy, knowing how to listen,...)
+
+**> Skills for life and emotional well-being:**
+Appropriate and responsible behaviors to face the challenges that we face, which allows us to organize our lives in a healthy and balanced way, facilitating experiences of satisfaction and well-being.
+
+
+# What is the Leader?
+
+> "Leadership means that a group, large or small, is
+willing to entrust authority to a person who has
+demonstrated ability, wisdom and competence.” 
+– Walt Disney
+
+- Not all company managers are leaders
+- There may be leaders withouth formal authority
+- The leader is elected by those who follow him.
+
+**Elements of leadership**
+- Leader and his followers
+- Influence (power) of the leader
+- Contributes to the achievement of objectives
+
+# Types of Leadership
+![[03-leadership 2022-04-21 16.52.09.excalidraw|1000x]]
+
+**> Autocratic**
+Commands and expects obedience. It tends to centralize authority and reinforce legitimate power (because of the position it occupies), reward power (reward) and coercive power (punish).
+
+**> Democratic**
+Escucha y consulta a los subordinados. Favorece la descentralización 
+
+**> Liberal**
+ Do and let do. Delegate authority to subordinates and let them freely decide how to achieve set goals.
+
+# 04 Motivation
+
+It is an inner force that drives one to act because of the consequences that the action will have in satisfying the person's needs.
+
+Psychological process that produces the activation, direction and persistence of behavior in a person. 
+
+**> Internal Factors**
+- **Needs** (e.g., paying for housing)
+- **Interests** (e.g., hobby in electronics, mechanics, etc.)
+- **Attitude** (e.g., satisfaction with a job well done)
+
+**> External Factors**
+- **Requests** (eg: ask for punctuality)
+- **Sanctions** (ex: 2 days without employment or salary)
+- **Praise** (ex: congratulations on reaching a goal)
+- **Money** (ex: productivity bonus)
+
+
+
+**> Maslows Pyramide**
+
+
+# 05 Communication
+
+# Communication Purposes
+- Communicate Facts
+- Persuade
+- Communicate Opinions
+- Communicate experiences and feelings
+
+# Communication Obstacles
+
+- Semantics
+- Communication Medium
+- Communication Channel
+- Attitude and Conduct

Areas/upv/classes/empresario/06-leading/01-managing-or-leading.md

@@ -1,9 +0,0 @@
-# Managing or Leading?
-
-It is said that on one occasion Jack Welch, CEO of General Electric, summoned his immediate subordinates, gave them a maximum of three words:
-
-> "Don't lead, lead!"
-
-and then left the room. Many of them were plunged into absolute confusion:
-
-> "What is the difference?"

Projects/plantarium/index.md

@@ -1,27 +0,0 @@
-# Plantarium
-
-Hi :)
-
-This guide will help you understand how Node based Interfaces work in general, and how the Plantarium Nodesystem works.
-
--> Lets get started.
-
-I like to think of Nodesystem as little factories connected by pipes. Each Node, or Factory gets some inputs, transforms  them and outputs something new.
-
--> Okay...?, Understood!
-
-Alright, who wants a coffee?
-
--> Mee!, No thanks...
-
-Well then, what do we need to make a coffee? A coffee machine of course!
-
-You can create one by pressing [shift+a] and search for *machine*.
-
-We also need someone who can consume our coffee, lets add a human.
-
-Now its time to connect these two nodes.
-
-![[index 2022-05-16 08.43.59.excalidraw]]
-
-

Resources/allgorithm/l-systems/index.md

@@ -0,0 +1,26 @@
+# L-Systems
+
+An L-System is an allgorithm that rewrites strings of text over and over again using predetermined rules.
+
+## Alphabet
+
+The set of all characters that are allowed in an L-System.
+
+*Example:* 
+- **[A,B]**
+
+## Axiom
+
+The initial text the L-System starts out with, for 
+
+*Example* 
+- **A**
+
+## Rule set
+
+The rules that are applied in each generation to the text. 
+
+*Example:*
+
+- **A** becomes **ABA**
+- **B** becomes **BBB**

Resources/electricity/active-components/op-amp-circuits.md

@@ -30,7 +30,7 @@ $$
 
 Because $V_-$ is equal to $V_+$ and 
 
-$V_- = V_s = V_o (\frac{R_g}{R_G+R_F})$
+$V_- = V_s = V_o (\frac{R_G}{R_G+R_F})$
 
 If we solve that equation for $\frac{V_O}{V_s}$ we get the following formula:
 

Resources/electricity/formulas.md

@@ -2,29 +2,34 @@
 cards-deck: electricity
 ---
 
-# Ohms Law #card
+## Ohms Law 
 
-*Solve for voltage:* #card
+*Solve for voltage:* 
+#card
 
 $\displaystyle V = I*R$
-^1654443735379
+^1654598090369
 
-*Solve for resistance:* #card
+*Solve for resistance:* 
+#card
 
 $\displaystyle R = \frac{V}{I}$
-^1654443831648
+^1654598090389
 
-*Solve for current* #card 
+*Solve for current* 
+#card
 
 $\displaystyle I = \frac{V}{R}$
-^1654443831659
+^1654598090398
 
-# Resistors in Series #card
+## Resistors in Series 
+#card
 
 $R = R1 + R2 + R3 ...$
-^1654443735407
+^1654598090404
 
-# Resistors in Parallel #card
+## Resistors in Parallel 
+#card
 
 $$
 \begin{flalign}
@@ -37,14 +42,17 @@ $$
 $$
 ***Tip:***
 If resistors of the same value are in parallel the total resistance is a single resistor divided by the amount if resistors.
-^1654443735425
+## Voltage Divider
+#card 
+^1654598090410
+
+$V_{out} = V_{in}(\frac{R_{1}}{R_1+R_2})$
 
 ## Thevenin’s Theorem 
 States that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load.
 
-# Kirchhoff's Law
+## Conservation of Charge (First Law) 
-
+#card
-## Conservation of Charge (First Law) #card 
 
 All current entering a node must also leave that node
 $$
@@ -52,8 +60,8 @@ $$
 \sum{I_{IN}} = \sum{I_{OUT}}&&
 \end{flalign}
 $$
-^1654443735443
 **Example:**
+^1654598090415
 
 ![](kirchhoffs-law-01.svg)
 
@@ -67,11 +75,13 @@ All the potential differences around the loop must sum to zero.
 $\displaystyle \sum{V} = 0$
 
 ## Capacitors in Series
+#card 
 
 $\displaystyle \frac{1}{C_{t}} = \frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} ...$
+^1654598090421
 
-### Impedance in a Circuit #card 
+## Impedance in a Circuit 
-
+#card 
 $$
 \begin{flalign}
 &Z = \sqrt{R^2 + X^2} &\\\
@@ -79,69 +89,70 @@ $$
 &X = X_{L} - X_{C} \\ 
 \end{flalign}
 $$
-^1654444201375
+## Capacitive Reactance 
-
+#card
-# Capacitive Reactance #card
+^1654598090426
 
 $\displaystyle X_{c} = \frac{1}{2 \pi fC}$
-^1654444201382
 
-# Inductive Reactance #card
+## Inductive Reactance 
+#card
 
 $\displaystyle X_{l} = 2\pi fL$
-^1654444201388
+^1654598090432
 
-# Analog Filters
+## Analog Filters
 
 ## Cutoff Frequency for RC Filters 
+#card 
 
 $\displaystyle f_{c} = \frac{1}{2\pi RC}$
+^1654598090437
 
 ## Cutoff Frequency for RL Filters
+#card
 
 $\displaystyle f_{c} = \frac{R}{2\pi L}$
-
+^1654598090445
-## Signal Response of an RC/RL Filter
-
-$X_c$ = [[#Capacitive Reactance]] || [[#Inductive Reactance]]
-
-$\displaystyle V_{out} = V_{in}(\frac{X_{c}}{\sqrt{R^2+X_{c}^2}})$
 
 ## Cutoff Frequency for multiple Low Pass Filters
-
 $\displaystyle f_{(-3db)} = f_{c}\sqrt{2^{(\frac{1}{n})}-1}$
 
 Where $n$ = Number if **identical** filters
 
 ## Resonance Frequency for RLC Low Pass Filter
+#card 
 
 $\displaystyle f_{o} = \frac{1}{2\pi \sqrt{LC}}$
+^1654598090452
 
 ## Center Frequency with Fc and Fh
+#card 
 
 $f_{c} = \sqrt{f_{h}*f_{l}}$
+^1654598090459
 
-## Filter Response for RC Filters #card 
+## Filter Response for RC Filters 
+#card
 
 $V_{out} = V_{in}(\frac{X_c}{\sqrt{R_{1}^2+X_{c}^2}})$
-^1654442437438
+^1654598090466
 
 ## Cutoff Frequency $\pi$ Topology Filter
+#card 
 
 When the two capacitors have the same capacitance, it can be calculated like this:
+^1654598090479
 
 $\displaystyle f_c = \frac{1}{4\pi\sqrt{LC}}$
 
-# Voltage Divider
+## Angular Frequency ($\omega$) 
-
+#card
-$V_{out} = V_{in}(\frac{R_{1}}{R_1+R_2})$
-
-# Angular Frequency ($\omega$) #card
 
 $\omega = 2\pi f = \frac{2\pi}{T}$
-^1654444201395
+^1654598090492
 
-# RLC Series Response
+## RLC Series Response
 
 This is basically Ohms Law:
 
@@ -154,25 +165,27 @@ $Z = \sqrt{R^2 + (X_L - X_C)^2}$
 $X_L$ = Reactive Inductance
 $X_C$ = Reactive Capacativw 
 
-# Current through a transistor
+## Current through a transistor
  
 $\displaystyle I_{EQ} = \frac{V_{BB}-{V_{BE}}}{\frac{R_B}{(\beta+1)}+R_E}$
 
-# Gain Bandwidth Product
+## Gain Bandwidth Product 
+#card 
+
 $GBP = A_V * f_c$
+^1654598090498
 
 $\displaystyle f_c = \frac{GBP}{A_V}$
 
-
+## Bandwidth of Multiple OpAmps
-# Bandwidth of Multiple OpAmps
 
 Where $n$ = number of stages
 and $BW$ = Bandwidth of single op-amp
 
 $BW_E = BW\sqrt{2^\frac{1}{n}-1}$
 
-
+## Power lost in a Resistor
-# Power lost in a Resistor
+#card 
 
 $P = IV = I^2R = \frac{V^2}{R}$
-
+^1654598090504

Resources/electricity/glossary.md

@@ -83,8 +83,7 @@ The Transfer function is a mathematical model of some analog filter that represe
 
 # Angular Frequency ($\omega$)
 
-
+![[formulas#Angular Frequency omega card]]
-![[formulas#Angular Frequency omega]]
 
 # Galvanic Isolation
 Galvanic isolation is a design technique that separates electrical circuits to eliminate stray currents

Resources/electricity/impedance.md

@@ -45,7 +45,7 @@ o 0 16 0 159746 10 0.0001 0 2 0 3
 
 When we drop the input resistance, the voltage that is provided to our circuit drops.
 
-We can use the voltage divtider equation to calculate the voltage that is available to the circuit:
+We can use the voltage divider equation to calculate the voltage that is available to the circuit:
 
 ![[voltage-dividers#Simple Voltage Divider#Equation]]
 
@@ -71,7 +71,6 @@ x 64 88 95 91 4 12 circuit
 
 If we play with the resistance slider on the right side
 
-
 # Impedance Matching
 
 Normally the input impedance should be much higher than the output impedance. But in certain cases we want the two to match.

Resources/electricity/passive-components/filters.md

@@ -14,7 +14,7 @@ Passive filters use passive components like resistors, capacitors or inductors.
 
 # Active Filters
 
-Aktive filters use active components like op-amps or transistors, active filters may be a bit better.
+Active filters use active components like op-amps or transistors, active filters may be a bit better.
 
 
 # Filter Types
@@ -27,7 +27,7 @@ Aktive filters use active components like op-amps or transistors, active filters
 ## Notch Filter
 
 
-# [[Resources/electricity/glossary#Cutoff Frequency|Cutoff Frequency]]
+# [[Resources/electricity/glossary#Cutoff Frequency f_ c|Cutoff Frequency]]
 
 ![[cutoff-frequency.png]]
 
@@ -47,7 +47,7 @@ We have a RC LFP which looks like this:
 
 First lets calculate the [[Resources/electricity/glossary#Cutoff Frequency|Cutoff Frequency]] with the specified formula:
 
-![[formulas#Cutoff Frequency for RC LowPass]]
+![[formulas#Cutoff Frequency for RC Filters]]
 
 $\displaystyle f_{c} = \frac{1}{2\pi300*0.000001}$
 
@@ -58,4 +58,11 @@ Now lets calculate the cutoff frequency when we place three of those filters in
 ![[formulas#Cutoff Frequency for multiple Low Pass Filters]]
 
 $f_{(-3db)} = 530.51 \sqrt{2^{(\frac{1}{3})}-1}$
-$\displaystyle f_{(-3db)} \approx 270.467010633$
+$\displaystyle f_{(-3db)} \approx 270.467010633$
+
+
+# Duty Cycle
+
+A duty cycle is the fraction of one period when a system or signal is active. We typically express a duty cycle as a ratio or percentage. A period is the time it takes for a signal to conclude a full ON-OFF cycle.
+
+![[duty_cycle.png]]

Resources/mathematics/geometry/euclidean.md

@@ -11,7 +11,7 @@ We know that the dot product of these two vectors must be zero, we can use that
 
 $V_1 \cdot V_2 = 0$
 
-Lets plugin our numbers
+Let's plug in our numbers
 
 $1 * V_2x + 6 * V_2y + 2 *V_2z = 0$
 

Resources/mathematics/linear-algebra/gauss.md

@@ -0,0 +1,27 @@
+# Gausses Method
+
+## Theorem
+If a linear system is changed to another by one of these operations:
+
+1. an equation is swapped with another
+2. an equation has both sides multiplied by a non zero constant.
+3. an equation is replaced by the sum of itself and a multiple of another
+
+→ Then the two systems have the same set of solutions.
+
+## Definition
+The three operations from the theorem are the *elementary reduction operations*, or *row operations*, or *Gaussian operations*.
+
+They are *swapping*, *multiplying by a scalar* and *row combination*
+
+## Solution Space
+
+### Systems without a unique solution
+
+When using gausses method and in the echelon form the linear system produces something like $0 = -1$ we know the system does not have a solution.
+
+### Systems with infinitely many solutions
+
+When we do not have a single $variable = constant$ stage in the echelon form we know we have infinitely many solutions.
+
+When one of the rows is $0 = 0$ or $1 = 1$ etc. we know that one of the input rows contained redundant information.

Resources/mathematics/linear-algebra/homework/gaussian-method.md

@@ -0,0 +1,94 @@
+# Gaussian Method
+
+## 1.17 Solving 
+
+### a.
+$$
+\begin{flalign}
+
+2x + 3y &= 13 &\\\
+x - y &= -1\\
+
+&\rightarrow (2p2 - p1) &\\\
+
+   5y &= 15 \\
+x - y &= -1 \\
+
+&\rightarrow (\text{swap } p1 / p2) &\\\
+
+x - y &= -1 \\
+   5y &= 15 \\
+\\
+y &= 3 \\
+x &= 2 \\
+
+\end{flalign}
+$$
+
+### b.
+
+$$
+\begin{flalign}
+ x -     z &= 0 &\\\
+3x + y     &= 1 \\
+-x + y + z &= 4\\
+\\
+\rightarrow& p3 + p1 \\
+ x -     z &= 0 \\
+3x + y     &= 1 \\
+         y &= 4\\
+\\
+x = -1\\
+y = 4\\
+z = -1
+\end{flalign}
+$$
+
+## Finding type of solutions
+
+## 1.18
+### a.
+
+$$
+\begin{flalign}
+−3x + 2y &= 0 &\\\
+−2y &= 0 \\
+&\rightarrow \text{One solution}
+\end{flalign}
+$$
+### b.
+
+$$
+\begin{flalign}
+x + y &= 4 &\\
+y − z &= 0 \\
+&\rightarrow \text{Infinitely many, now row leading with z}
+\end{flalign}
+$$
+
+
+$$
+\begin{flalign}
+−3x + 2y &= 0 &\\\
+−2y &= 0 \\
+&\rightarrow \text{One solution}
+\end{flalign}
+$$
+## 1.19
+
+## a.
+$$
+\begin{flalign}
+2x +  2y  &=  5  &\\\
+x  -  4y  &=  0 \\
+
+\rightarrow & -\frac{1}{2}p1 + p2 \\
+
+2x +  2y  &=  5  &\\\
+   - 5y &= -2.5 \\
+\\
+y &= \frac{1}{2}\\
+x &= 2
+
+\end{flalign}
+$$

Resources/mathematics/linear-algebra/index.md

@@ -0,0 +1,16 @@
+# Linear Algebra
+
+**Linear systems** are a combination of variables and *coefficients* they look like this:
+
+$a_1x_1 + a_2x_2 + a_3x_3 ... a_nx_n$
+
+Where $a_1...a_n$ are the *coefficients*.
+
+
+**Linear equations** are almost the same but with an equal sign and a *constant* on the right side like this.
+
+$a_1x_1 + a_2x_2 + a_3x_3 ... a_nx_n$
+
+We want to solve these by finding real numbers for $x_1 ... x_n$ that satisfy the equation.
+
+

Resources/psychology/learning.md

@@ -0,0 +1,3 @@
+# Learning
+
+